
Class rrxod 

B()ok_lMM 

( 'Op^Tiglil N^ 



COFYRKIHT DEPOSIT. 



WORKS OF 
PROF. WALTER L. WEBB 



PUBLISHED BY 



JOHN WILEY & SONS. 



Railroad Construction.— Theory and Practice. 

A Text-book for the Use of Students in Colleges 
and Technical Schools. Third Edition. Revised 
and Enlarged. i6mo. xvi + 727 pages and 232 
figures and plates. Morocco, $5.00. 

Problems in the Use and Adjustment of Engineer- 
ing Instruments. 

Forms for Field-notes ; General Instructions for 
Extended Students' Surveys. i6mo. Morocco, 
$1.25. 

The Economics of Railroad Construction. 

Targe i2mo. viii -J- 3 39 pages, 34 figures. Cloth, 
$2.50. 



THE ECONOMICS 



OF 



RAILROAD CONSTRUCTION 



BY 

WALTER LORING WEBB, C.E. 

Member American Society of Civil Engineers ; Member American Railway 

Engineering and Maintenance of Way Association; 

Assistant Professor of Civil Engineering (Railroad Engineering) 

in the University of Pennsylvania, 1893-1901 ; etc. 



FIRST EDITION 
FIRST THOUSA^^D 



NEW YOEK 

JOHN WILEY & SONS 

Loi^^DON^: CHAPMAN & HALL, Limited 

1906 



LIBRARY of CONGRESS 
Tw« Ce»iM Rtctived 

SEP 28 t906 

n Ctpyfif V Entry 
CLASS A XX^M Ha. 
COFY B. f' 



x.<> 



Copyright, 1906 

BY 

WALTER LORING WEBB 




ROBERT DRUMMOND, PRINTER. NEW YORK 



CONTENTS. 



PAGE 

Introduction 3 



PART I. FINANCIAL AND LEGAL ELEMENTS 
OF THE PROBLEM. 

CHAPTER I. 

Railroad Statistics 4 

Mileage, 4. Capitalization, 10. Public service of railways, 
11. Employees^ 12. Accidents, 12. Use of statistical 
averages, 14. 

CHAPTER II. 

The Organization of Railroads 16 

Economic justification of railroad projects, 16. Basis of 
ownership of railroad property, 17, Charters, 19, General 
railroad lav;5, 20. General railroad lavv^ of the State of New 
York, 21. 

CHAPTER III. 

Capitalization. 25 

Stock, 25. Funded debt, 26. Dividends on stock, 29. 
Interest on bonds, 31= Taxes, 32. Small margin between 
profit and loss, 33. Variation in dividends due to small 
variations in business done, 36. Practical limitations of 
capitalization. 38. Principles which should govern the 
amount of capital to be raised, 39. 

iii 



iv CONTENTS. 

CHAPTER IV. 

PAGE 

The Valuation of Railway Property 41 

Objects, 41. Nominal valuation, 41. Cost-of-replacing- 
property method, 43. Valuation of physical properties and 
franchise, 45, Stock-market valuation, 47. Valuation by 
capitaHzing the net earnings, 47. Legal Control, 52. 
Basis of freight-rates, 52. Direct competition, 55. Indirect 
competition, 56. Justification of special commodity rates, 
58. Low rates on low-grade freight, 32. Federal Control: 
Origin, 59. Necessity for control, 60, Pooling, 61. Trafiic 
associations, 62. Consolidation, 63. State Control: Scope 
and Umitations, 64. 

CHAPTER V. 

JESTIMATION OF VoLUME OF TRAFFIC 66 

Primary considerations, 66. Methods of estimating volume 
of traffic, 68. Estimate of earnings per mile of road, 70. 
Estimate of tributary population, 72. Estimate by compar- 
ison with other roads, 73. Actual estimation of the sources 
of revenue, 74. Estimation of passenger traffic, 75. Condi- 
tions WHICH Affect Volume of Traffic: Proximity to 
sources of traffic, 78. Estimation of effect of location of 
station at a distance from a business center, 80, Extent of 
monopoly in railroad business, 81. 

PART IL OPERATING ELEMENTS OF THE PROBLEM. 

CHAPTER VI. 

Operating Expenses. . 83 

Classification of operating expenses, 83. Average operatmg 
expenses per train-mile, 83. Itemized classification of oper- 
ating expenses, 87. Maintenance of Way and Structures: 
Item I. Repairs of roadway, 92. Item 2. Renewals of rails, 
93. Item 3. Renewals of ties. 93. Item 4. Repairs and re- 
newals of bridges and culverts, 94. Items 5 to 10. Repairs and 
renewals of fences, road-crossings, and cattle-guards — of 
buildings and fixtures — of docks and wharves — of telegraph- 
plant; stationery and printing, and ''other expenses," 94. 
Maintenance OF Equipment. Item 11. Superintendence, 95. 
Item 12. Repairs and renewals of locomotives, 95. Items 13, 



CONTENTS. V 

PAGE 

14, and 15. Repairs and renewals of passenger-cars — of freight- 
cars — and of work-cars, 97. Conducting Transportation; 
Item 20. Superintendence, 98. Item 21. Engine- and round- 
house-men, 98. Item 22. Fuel for locomotives, 100. Items 
23, 24, and 25. Water-supply; oil, tallow, and waste; other 
supphes for locomotives, 101. Item 26. Train service, 101. 
Item 27. Train supplies and expenses, 102. Items 28, 29, 
30, and 31. Switchmen; flagmen and watchmen; telegraph 
expenses; station service and station supplies, 102, Item 32. 
Switching charges, 103. Item 33. Car per diem and mileage 
— balance, 103. Items 35, 36, and 37. Loss and damage; 
injuries to persons; clearing wrecks, 105. Items 38 to 53, 
105. Estimation of the effect on operating expenses of a 
change in alinement, 105. Reliability of such estimates, 106. 

CHAPTER VII. 

Motive Power 109 

Economics of the Locomotive: Total cost of power by the 
use of locomotives, 109. Renewals of locomotives, 110. 
Repairs of locomotives, 112. Wages of engine- and round- 
house-men, 115. Fuel for locomoti^^es, 117. Water-supply — 
impurities, 120. Methods of water purification, 123. Pump- 
ing water, 124. Oil, tallow, and waste for locomotives, 125. 
Comparative cost of various types of locomotives, 126. The 
Economics of Heavy Locomotives: The problem stated, 
127. Economy effected by handling a given traffic with one 
less train, 129. Maintenance of way, 130. Maintenance of 
equipment, 131. Conducting transportation, 133. Numer- 
ical illustration, 136. 

CHAPTER VIII. 

Economics of Car Construction 138 

Weight of cars, 139. Ratio of live load to dead load, 139. 
Economics of high-capacity cars, 140. Use of air- or train- 
brakes, 142. Use of automatic couplers, 143. Draft-gear, 
143. Spring draft-gear, 144. Friction draft-gear, 147. 

CHAPTER IX. 

Track Economics 151 

Rails: Rail wear — theoretical, 151. Rail wear — statis- 
tics, 154. Rail-wear statistics on the Northern Pacific R. R., 



VI CONTENTS. 

PAGE 

156. Relation of rate of rail wear to the life-history of the 
rail, 158. Rail wear on curves, 160. Economics of Ties; 
Importance of the subject. 163. Methods of deterioration 
and failure of ties, 163. The actual cost of a tie, 164. Chem- 
ical treatment of ties, 166. Comparative value of cross-ties 
of different materials, 167. Protection against wear by- 
using tie-plates, 173. Use of screw-spikes, 174. 

CHAPTER X. 

Train Resistance 178 

Classification of the various forms, 178. Resistances in- 
ternal to the locomotive, 179. Velocitj'' resistances. 180. 
Wheel resistance, 182. Grade resistance, 184. Curve resist- 
ance, 187. Brake resistance, 188. Inertia resistance, 189. 
Train-resistance formulae, 192. Comparison of the above 
formulae, 196. Dynamometer tests, 197. 

CHAPTER XI. 

Momentum Grades 200^ 

Velocity head, 200. Practical use of Table XX, 202. 
Accuracy of the above statement, 204. Utilization of Table 
XX, 207. Momentum Diagrams and Tonnage Ratings: 
Tonnage rating, 209.. Tonnage rating of locomotives, 209. 
Tonnage rating for a given grade and velocity, 211, Accelera- 
tion curves, 213. Retardation curves, 217. Practical utili- 
zation of these diagrams, 219. Another tonnage-ratmg 
formula (Henderson), 223. 



PART III. PHYSICAL ELEMENTS OF THE PROBLEM. 

CHAPTER XII. 

Distance 225 

Relation of distance to rates and expenses, 225. The 
conditions other than distance that affect the cost; reasons 
why rates are usually based on distance, 226. Variable 
effect on expenses of extent of change in distance, 227. 
Ei'FECT OF Distance on Operating Expenses: Effect of 
changes in distance on maintenance of way, 228. Effect on 
maintenance of equipment, 230. Effect on conducting trans- 



CONTENTS. vii 

PAGB 

portation, 234. Item 21. Wages of engine- and roundhouse- 
men, 234. Item 22. Fuel, 234. Items 23, 24, and 25. 
Minor engine-supplies, 237. Item 27. Train-supplies and 
expenses, 238. Item 28. Switchmen, flagmen, and watchmen, 
238. Item 29. Telegraph expenses, 238. Item 33. Car- 
mileage, 239. Items 35, 36, and 37. Expenses and damage, 
240. Estimate of total effect on expenses of small changes in 
distance (measured in feet); also estimate for distances 
measured in miles, 240. Effect of Distance on Receipts: 
Classification of traffic, 241. Method of division of through 
rates between the roads on which through traffic is carried, 
242. Effect of a change in the length of the road on its 
receipts from through-competitive traffic, 244. Application 
of the above principle, 246. General conclusions regarding a 
change in distance, 246. Justification of decreasing distance 
to save time, 248. Effect of change of distance on the business 
done, 248. 



CHAPTER XIII. 

Curvature 250 

General objections to curvature, 250. Financial value of 
the danger of accident due to curvature, 251. Effect of 
curvature on traffic, 252. Effect of curvature on the operation 
of trains, 253. Limiting the use of heavy engines, 254. 
Effect of Curvature on Operating Expenses: Relation 
of radius of curvature and of degrees of central angle to 
operating expenses, 254. Effect of curvature on maintenance 
of way, 257. Item 1. Repairs of roadway, 258. Item 2. 
Renewals of rails, 258. Item 3. Renewals of ties, 259. 
Effect of curvature on maintenance of equipment, 259. Item 
12. Repairs and renewals of locomotives, 259. Items 13, 14, 
and 15, 260. Item 17. The repairs and renewals of shop 
machinery, 260. Effect of curvature on conducting trans- 
portation, 261. General expenses, 262. Estimate of total 
effect per degree of central angle, 262. Numerical illustra- 
tion, 264. Reliability and value of the above estimate, 267. 
Compensation for Curvature: Reasons for compensation, 
268. The proper rate of compensation, 271. The limitations 
of maximum curvature, 273. 



Viil CONTENTS. 



CHAPTER XIV. 

PAGE 

Minor Grades 2/6 

Two distinct effects of grade, 276. Basis of the cost of 
minor grades, 278. Meaning of ''rise and fall," 279. Classi- 
Ication of minor grades, 281. Effect on operating expenses, 
283. Item 1. Repairs of roadway, 283. Item 2. Renewals 
of rails, 283. Item 3. Renewals of ties, 284. Maintenance 
of equipment, 284. Conducting transportation, 285. Esti- 
mate of cost of one foot of change of elevation, 285. 
Numerical illustration, 286. 



CHAPTER XV. 

Ruling Grades 289 

Definition, 289. Choice of ruling grade, 290. Maximum 
train-load on any grade, 291. Financial value of increasing 
the train-load, 295. Maintenance of equipment, 296. Con- 
ducting transportation, 298. Numerical illustration, 300. 



CHAPTER XVI. 

Pusher Grades 303 

General principles underlying the use of pusher-engines, 303. 
Numerical illustration of the general principle, 304. Equating 
through grades and pusher grades, 305. Method of operation 
of pusher grades, 310. Length of a pusher grade, 314. The 
cost of pusher-engine service, 314. Numerical illustrations of 
the cost of pusher service, 316. 



CHAPTER XVII. 

Balancing Grades for Unequal Traffic 319 

Nature of the subject, 319. Illustrations in the balancing 
of grades, 320. Principles on which the theoretical balance 
must be computed, 320. Numerical illustration, 322. Re- 
liability of calculations of this nature, 323. 

Index 325 



THE 
ECONOMICS OF MILEOAD CONSTEUCTION. 



INTRODUCTION. 

Owing to the diversity of opinion existing among rail- 
road men as to the proper scope of a book on railroad 
economics, a word of introduction is necessary. Railroad 
economics, in its broadest sense, covers the entire subject 
of railroad engineering, from the most simple feature of 
railroad surveying to the weightiest questions of railroad 
practice or legislation which could be brought before the 
Interstate Commerce Commission, Congress, or the United 
States Supreme Court. While it is of course desirable 
that an engineer should have as broad a knowledge as 
possible of every phase of railroad management and legis- 
lation, it should not be forgotten that his primary work 
is that of construction, maintenance, and operation. If 
the railroad engineer should develop into the railroad 
president, the larger questions must be answered, but even 
in such a case an encyclopedia of railroad science would 
not cover the ground with which he should be familiar. 

It is assumed that those who read or study this book 
are already familiar with the mechanical processes used in 
railroad surveying and construction; that they know how 
to survey a line (when the economic questions of its loca- 
tion have been decided), and how to build a line as thus 



2 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

laid out. Of course many of the simpler economic prin- 
ciples will have been included in any good course in sur- 
veying and construction. But such courses do not usually 
include an exhaustive exposition of the reasons ivhy cer- 
tain grades should be adopted, or why a certain larg3 
expenditure for a tunnel, bridge, or other special con- 
struction may (or may not) be justifiable. The justifica- 
tion of improvements by changes in alinement also come ^ 
within the scope of the engineer. The constructing 
engineer should also know enough of the work of opera- 
tion to understand the effect on operation of constructive 
details. This requires a knowledge of operating expenses, 
locomotive and car construction, train-resistance, and the 
operation of heavy trains on grades. Even then the con- 
structive engineer is not equipped for his work until he 
has dipped into law and finance — until he understands the 
legal method of organization and the methods of the world 
of railroad finance. 

Rising still higher, the railroad man is sometimes con- 
fronted with an apparent conflict between a policy which 
would best serve the pubhc, and a policy which would afford 
greater immediate profit to the stockholders. Probably 
such conflicts are more apparent than real. History has 
invariably shown that the prosperity of a railroad is closely 
bound up with that of the community which it serves, and 
that in the long run the interests of the stockholders are 
best promoted by policies which give the best possible 
service to the public. 

This book is therefore written from the standpoint of 
the constructing or operating engineer. The railroad lawyer 
or legislator would find little or nothing in it which he can 
use, and much in which he is not interested. Even the 
professor of social economics will find that it is written 
from the technical standpoint rather than from the social 
viewpoint, and yet (as before mentioned) it will be em- 



INTRODUCTION. 6 

phasized that the best social standpoint will also prove 
to be the best technical standpoint. 

The practicable size of this book has also been consid- 
ered. An adequate discussion of railroad legislation alone 
would more than fill a book of this size. Therefore legis- 
lation and kinched subjects are only considered very 
briefly, and almost exclusively as they affect questions 
which must be answered by a railroad engineer. 

The author wishes to acknowledge his indebtedness to 
many engineers throughout the country who have fur- 
nished him with some very valuable technical information. 
The sources of such information have each been indicated 
during its discussion. 

Those famihar with recent railroad hterature, especially 
the books dealing with railroad legislation, the regulation 
of rates, etc., will appreciate the author's indebtedness to 
some of them. The chapters of this book dealing with 
kindred subjects attempt to give an abridged outhne of 
some of the most salient features of these valuable addi- 
tions to railroad science. For more complete discussions 
the student should read the following: ''Railway Legisla- 
tion in the United States," by Dr. B. H. Meyer; "Restric- 
tive Railway Legislation," by H. S. Haines; "American 
Railway Transportation," by E. R. Johnson; "The Ele- 
ments of Railway Economics," by W. M. Acworth; "Rail- 
road Transportation," by A. T. Hadley; and "American 
Railroad Rates," by W. C. Noyes. 



PAET I. 

FINANCIAL AND LEGAL ELEMENTS OF THE 
PROBLEM. 



CHAPTER I. 

RAILROAD STATISTICS. 

I. Mileage. — A study of the growth of railroad mileage 
during a period of years will reveal many instructive 
features of railroad progress. In the following chapter 
will be given several tables of statistics showing the growth 
of the railroad industry, especially during later years. 
From such tables it is possible to draw conclusions, regard- 
ing the present status of railroad business and its probable 
future growth, which will be of considerable value to the 
railroad engineer in understanding many of the problems 
which must be solved. But it should not be forgotten 
that the proper interpretation of statistics is not easy, 
and that wrong conclusions may readily be drawn from 
them. An endeavor will be made to point out some of 
the legitimate conclusions which these statistics indicate. 
In Table I is given the mileage in the United States for 
each year from 1870 to 1904, the increase for each year, 
the number of miles of line per 100 square miles of terri- 
tory, the number of miles of line per 10,000 inhabitants, 
and the total railway capital per mile of line. The figures 
for the year 1888 and later are taken from the reports of 
the Interstate Commerce Commission. Those for previous 

4 



RAILROAD STATISTICS. 5 

years have been taken from various sources, chiefly the 
annual issues of Poor's Manual. The figures given in the 
later issues of Poor's Manual do not agree exactly with 
those from the Interstate Commerce Commission, although 
the agreement is suflficiently close for any deductions 
which we may here wish to draw from the figures. It 
should be noted that the ^'number of miles of line " does 
not consider whether the road has one track, two, three, 
or four, nor that a mile of line in one place may be worth 
ten or twenty times a mile of line in some other place. 
The growth of the mileage may be most readily studied 
by an inspection of Fig. 1. The steeper the line, the more 
rapid has been the growth in mileage. The annual in- 
crease and its fluctuations are more readily seen in Fig. 2. 
For several years after the ^^boom " times of 1870 to 1873 
but little was done, until another boom began about 
1878-9. This culminated in 1882 and dropped suddenly 
in 1884-5. After the panic year of 1893 but little was 
done until 1898-9. Since that time there has been an 
almost steady increase in the number of miles added each 
year. It is hardly possible that this increase in growth 
can be long maintained. A steady growth each year is 
about as much as could be expected, while a decrease for 
a period of years is quite probable. 

The "number of miles of line per 100 square miles of 
territory " is shown graphically in Fig. 3. Since the area 
considered is constant, the number constantly increases 
The rate of growth is indicated by the steepness of the line 
or by the differences which are given in column 4 of Table 
I and are indicated graphically in Fig. 3. These vary 
approximately as the increase in the mileage. In column 
5 of Table I is shown the "number of miles of line per 
10,000 inhabitants." A glance at that column will show 
at once that for the last fifteen years the number is very 
nearly constant. The number reached a maximum in 



THE ECONOMICS OF RAILROAD CONSTRUCTION. 



1893. The check in railroad building caused by the panic 
of that year caused a gradual reduction in the ratio, which 
meant that the population was growing faster than the 
building of railroads. This tendency was not checked 
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Fig. 1. — Total railroad mileage in the United States. 

has so increased that it can afford more miles of railroad 
per 10,000 inhabitants. 

The ''total railway capital per mile of Hne " has re- 
mained fairly constant. Disregarding the value given for 
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RAILROAD STATISTICS. 



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8 THE ECONOMICS OF RAILROAD CONSTRUCTION. 




RAILROAD STATISTICS. 



Table I. — Railroad Statistics. 



1 


2 


3 


4 




5 


6 


Year. 


Mileage. 


Annual 
increase. 


Number of miles 

of line per 100 

square miles 

of territory. 


Number of 
miles of line 

per 10,000 
inhabitants. 


Total railway- 
capital per 
mile of line. 










Diff. 






1870 


52 914 


6,070 


1.78 


.25 
.20 
.14 
.07 
.06 


13.72 


$44,255 


71 


60,293 


7,379 


2.03 


15.18 


59,726 


72 


66,171 


5,878 


2.23 


16.19 


55,116 


73 


70,268 


4,097 


2.37 


16.71 


57,136 


74 


72,383 


2,117 


2.44 


16.76 


60,944 


1875 


74,096 


1,711 


2.50 


.09 
.07 
.09 
.16 
.23 


16.74 


61,534 


76 


76,808 


2,712 


2.59 


16.87 


60,791 


77 


79,089 


2,280 


2.66 


16.94 


60,699 


78 


81,776 


2,629 


2.75 


17.08 


58,916 


79 


86,497 


4,746 


2.91 


17.65 


58,070 


1880 


93,349 


6,886 


3.14 


.33 
.39 
.23 
.13 
.12 


18.61 


58,624 


81 


103,145 


9,796 


3.47 


20.06 


60,645 


82 


114,713 


11,568 


3.86 


21.77 


60,830 


83 


121,454 


6,741 


4.09 


22.51 


61,592 


. 84 


125,379 


3,825 


4.22 


22.71 


60,886 


1885 


128,967 


3,588 


4.34 


.25 
99 


22.83 


60,897 


86 


136,338 


7,371 


4.59 


23.61 


60,564 


87 


142,776 


6,438 


4.81 


.15 


24.19 


58,093 


*1888 


149,902 


7,126 


4.96 


9fi 


24.87 


59,392 


89 


157,759 


7,857 


5.22 


.29 


25.63 


58,775 


1890 


163,597 


5,838 


5.51 


Ifi 


26.05 


60,340 


91 


168,403 


4,806 


5.67 


1 1 


26.26 


60,942 


92 


171,564 


3,161 


5.78 


. 1 1 

.16 
.08 
.06 


26.22 


63,776 


93 


176,461 


4,898 


5.94 


26.43 


63,421 


94 


178,709 


2,247 


6.02 


26.25 


62,951 


1895 


180,657 


1,949 


6.08 


.07 
.06 
.07 
.09 
.14 


26.03 


63,206 


96 


182,777 


2,119 


6.15 


25.84 


59,610 


97 


184,428 


1,652 


6.21 


25.60 


59,620 


98 


186,396 


1,968 


6.28 


25.41 


60,343 


99 


189,295 


2,898 


6.37 


25.35 


60,556 


1900 


193,346 


4,051 


6.51 


.13 
.18 

.18 
.20 


25.44 


61,490 


01 


197,237 


3,892 


6.64 


25.52 


61,531 


02 


202,472 


5,234 


6.82 


25.76 


62,301 


03 


207,977 


5,505 


7.00 


26.03 


63,186 


04 


213,904 


5,927 


7.20 


26.34 


64,265 



_ * For 1888 and later, figures taken from reports of Interstate Commerce Com- 
mission. Earlier reports less reliable and accurate. 



10 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

surprising when we consider that every mile of railroad is 
far better and more valuable than it was twenty-five or 
thirty years ago. Evidently the capitalization is now a 
truer measure of actual worth than it was many years ago. 
If we multiply the corresponding numbers of columns 
5 and 6, and divide by 10,000, we would get ^'the total 
railway capital per inhabitant," which will vary from a 
minimum of about $61 per inhabitant in 1870 to $169 in 
1904. It may also be noted that one of the highest values 
of the total railway capital per inhabitant ($168) occurred 
immediately before the financial crash of 1893. For some 
reason the values of " total railway capital per inhabitant/' 
computed by the above method, are somewhat larger than 
the corresponding values as given in Table II ^ which are 
taken from U. S. Census Reports. The differences are 
not sufficiently large to alter any conclusions we may wish 
to draw from them. 

2. Capitalization. — Deferring until Chapter III an analy- 
sis of railway capital from the financial standpoint, it is 
instructive to note the total value of railway property 
and its relation to the total national wealth. In Table II 
is given for decennial periods the total national wealth, the 
wealth per inhabitant, and the corresponding average 
figures for railway property. 

Table II. — National Wealth and Railway Capital. 



Year. 


Total na- 
tional wealth, 


Population. 


Wealth per 
capita. 


Total rail- 
way capital, 


Railway 
capital 




millions. 




milhons. 


per capita. 


1850 


$ 7,136 


23,191,876 


$ 308 


$ 297* 


$ 13 


1860 


16,160 


31,443,321 


514 


1,156* 


36 


1870 


30,069 


38,558,371 


780 


2,041* 


53 


1880 


43,642 


50,155,783 


870 


5,108 


102 


1890 


65,037 


62,622,250 


1036 


9,437 


151 


1900 


94,300 


75,568,686 


1248 


11,491 


152 



Cost of construction. 



RAILROAD STATISTICS. 11 

It affords some idea of the magnitude of the railroad 
business of the country to note that if the total railway 
capitalization (stocks and bonds) in 1900 were divided 
equally among the total population, every man, woman, 
and child would have railroad securities of a par value of 
$152. It will be shown later that the " commercial value " 
of all the railroads for 1904 was about 85% of their par 
value. 

3. Public service of railways. — A few statements regard- 
ing the actual service rendered by railways will permit the 
student to better appreciate the influence which railroads 
have on our civilization. The statistics for the year end- 
ing June 30, 1904, may be considered as typical. The 
number of passengers reported as carried was 715,419,682, 
which means an average of nearly nine rides per capita. 
The average ride was over 30 miles, for which an average 
revenue of 2.006 cents per mile was received. The enor- 
mous volume of ''commutation- ticket " mileage is respon 
sible for the reduction of this figure from the usual charge 
of 3 cents per mile. The average number of passengers in 
a train was 46, with average receipts of $1.14 per passenger- 
train mile. 

The ''number of tons carried one mile " was 174,522,- 
098,577. Dividing this by the population, we have 2309 
ton-miles per capita. This means that every man, woman, 
and child would be responsible (if all were equally respon- 
sible) for the haulage of 2309 ton-miles or 23 tons of freight 
a distance of 100 miles. The average number of tons of 
freight in a train was 308, which was carried at an average 
charge of 0.78 cents per ton per mile. The revenue per 
freight- train mile was $2.44. The average revenue per 
train- mile for all trains was $1.94, while the average cost 
was $1.31. The passenger revenue comprised 22.50% of 
the total, and the freight 69.82%. The remaining 7.68% 
is divided between mail, express, and other miscellaneous 



12 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

earnings. The ^' total earnings from operation" were 
$1,975; 174,091, which was nearly 15% of the total capital- 
ization. These earnings represent over $24 per capita. 
In considering this large payment per capita, it should be 
realized that a considerable proportion of the cost of every 
ton of coal and, perhaps in lesser degree, of almost every 
article of manufacture and of farm and mineral products 
consists of the cost of transportation, which is paid in- 
directly to a dealer, if it is not paid directly to the railroad 
company. 

4. Employees. — 1,296,121 employees were carried on 
the rolls on June 30, 1904, or an average of 6.11 per mile 
of Une. There were paid to these employees $817,598,810 
which is over 41% of the gross earnings from operation 
or 61% of the total operating expenses. This number of 
employees represents nearly one-sixtieth of the population. 
Probably one-twentieth of the population was supported 
by these earnings. When we consider the number of 
locomotive shops, car shops, bridge shops, and factories of 
various kinds whose output is consumed in whole or in 
part by the railroads of the country, it is probably true 
that one-fourth of the entire population Hve on wages 
furnished directly by the railroads or by industries which 
are chiefly supported by railroads. 

5. Accidents. — During the year ending June 30, 1904, 
the numbers reported as killed and injured were 10,046 
and 84,155 respectively. This is an average of one person 
killed every 52 minutes and one person injured every 6 
minutes. While this statement looks very bad, the rail- 
roads are not altogether responsible. Of the total 10,046, 
only 441 (a little over 4%) were passengers; 3632 (about 
36%) were employees; and the remainder, 5973, were 
''other persons," of whom 5105 (over 50% of the total) 
were " trespassers," which includes suicides. Therefore the 
ailroads cannot be held responsible for over one-half of 



RAILROAD STATISTICS. 13 

those deaths. Of the 84,155 persons injured, the number 
of passengers was 9111, or about 11%, and the number of 
employees 67,067, about 80%. About one-sixth of the 
deaths, and about one-eighth of the injuries, of passengers 
were caused by '^jumping on or off trains, locomotives, or 
cars." In nearly all of such cases the passengers were 
alone responsible. 

In the face of such a death-list, it is hard to realize the 
very small probability of an injury or death occurring to 
any passenger during any one ride. The ^'number of pas- 
sengers carried one mile " for 1904 equaled 21,923,213,536. 
Dividing this by 441, the number of deaths of passengers, 
we have over 49,700,000, the number of passenger-miles for 
each death. Again, dividing 21,923,213,536 by 9111, the 
number of passengers injured, we have over 2,400,000 as 
the number of passenger-miles for each injury. The prac- 
tical meaning of such figures is that, in the language of 
the theory of probabilities, the '^chances are even" that 
if a passenger were to ride continuously at the rate of 40 
miles per hour, or 350,640 miles per year, he would ride for 
142 years before being killed, or about 7 years before being 
injured. But, as a matter of fact, no one uses the railway 
for a distance of 350,000 miles per year, or even any large 
proportion of it. A better way of considering the prob- 
abilities would be to say that, since there were 49,700,000 
passenger-miles for each death, a trip of say 100 miles 
would involve a risk of one in 497,000 that it might result 
in death, assuming that the operation of the railroad 
during that trip was neither more nor less hazardous than 
the average railroad operation. A similar figure could be 
computed to determine the probability that an}^ given 
trip might result in an injury to any given passenger. It 
should not be forgotten that during the year 1904 a far 
greater number of passengers were killed than during any 
year for the previous 16 years. In 1895 the number of 



14 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

passengers killed was only 170, which was less than 40% 
of the figure for 1904. Although the amount of raihvay 
business was far greater in 1904 than in 1895, and we 
might expect some increase in the fatalities, yet the proba- 
bilities were far less in 1895 than in 1904. 

There has been much discussion of the subject of acci- 
dents as an element in railroad economics. Some econ- 
omists have endeavored to place a financial value on 
accidents and to determine how much money could profit- 
ably be spent to avoid the danger of accidents. While no 
one will deny the justification of spending a reasonable 
amount of money to avoid the danger of an accident due 
to some specific cause, the question always remains. How 
much actual lessening of danger will be accomplished by 
any reasonable or practicable expenditure of money? 
Certain classes of improvements are demonstrably justifi- 
able, as, for example, the elimination of grade highway- 
crossings, especially on a road of heavy traffic. A more 
doubtful question occurs when it is proposed to reduce 
some sharp curvature when passing through a mountainous 
region where the view of the track is obstructed for any 
great distance. In such a case the practical question is 
not the lessening of danger by the elimination of all curva- 
ture, which would probably be financially, if not physically, 
impossible, but the lessening of danger by the use of less 
curvature rather than more. It may usually be shown 
that the lessening of the probability of accidents, due to 
such reductions of curvature as are practicable, is so small 
that such a consideration alone will not justify the expen- 
diture of any appreciable amount of money to accomplish 
the result. 

6. Use of statistical averages. — The student should be 
cautioned against an improper use of the statistical aver- 
ages given in this chapter and in Chapter VI. They 
should be considered somewhat in the same light as a 



RAILROAD STATISTICS. 15 

composite photograph of a group of men. The composite 
photograph cannot be considered as a correct photograph 
of anyone, unless he happens to have the average features. 
The above averages regarding wealth per capita, railway 
capital per capita, and the average payment to railroads 
per capita should not be assumed to have any appHcation 
to any particular case. For example, the student should 
not consider that the average annual payment as given 
for 1904 — $24 per capita — would represent the earnings 
of any proposed railroad from its tributary population, 
unless there is good reason to believe that the particular 
territory in question is a fair average sample of the whole 
country. And even in this case the determination of the 
'tributary population " is not easy. Such a figure has its 
value to give the student a rough idea of railroad earnings 
and railroad operation, but he should know that such 
figures cannot be depended on, except as a rough check on 
computations which have been more carefully made from 
local considerations. 



CHAPTER II. 

THE ORGANIZATION OF RAILROADS. 

7. Economic justification of railroad projects. — Social 
economists and railroad capitalists are apt to consider the 
desirability of constructing the railroad from two different 
points of view. The social economist considers chiefly the 
effect of the road in building up the wealth of the com- 
munity through which it passes. The railroad capitalist 
looks on the whole project as a business enterprise and as 
a project for making money. It may readily be demon- 
strated that in the long run the two objects are really 
identical and require identical methods to arrive at the 
result. Of course there are cases where a railroad enter- 
iprise has been launched for the purpose of blackmailing 
another competing line, and there are hkewise many 
cases where the promoters intend to unload their securities 
at the first favorable opportunity, and have no thought of 
the future history of the road or the ultimate value of 
its securities. Disregarding such methods, which may be 
characterized as gigantic swindles, we may consider that 
the normal project of constructing a railroad consists in 
developing a transportation agency which will not only 
increase the wealth of the country, but which will itself 
derive profit from the increasing wealth of the country, 
and that the wealth of each will increase the wealth of the 
other almost without definite limit. The prosperity of the 
railroad project and of the country through which it passes 
will be mutually dependent. We may therefore disregard 
at the outset the idea that any policy of construction or 

16 



THE ORGANIZATION OF RAILROADS. 17 

management which would be beneficial to the road will 
be injurious to the community. Of course it may readily 
happen, and instances are numerous, especially with roads 
of considerable length, that the cities and industries of one 
section of the road will be built up at the expense of those 
of another, and that the policy which is really the most 
advantageous for the railroad as a whole may be injurious 
to the interests of a small section of the country through 
which it passes. Even here, we should not forget that the 
railroad has lost something, although it may have gained 
more. It has lost a portion of traffic which it might have 
obtained by the building-up of the section which has been 
slighted and perhaps really injured. 

The organization of a railroad always begins essentially 
with the idea that a road built through a certain stretch 
of country will be a paying investment. It also proceeds 
on the basis, which is often not realized, that it should 
and will be a paying investment to the original promoters. 
It is unfortunately true that but few railroads which are 
old enough to have had a history have escaped a receiver- 
ship, or at least serious financial difficulties, at some time 
in their history. Nevertheless, the fundamental idea of 
the enterprise is that it shall be financially profitable to 
the promoters of the road. 

8. Basis of ownership of railroad property. — A railroad 
enterprise is fundamentally different from a large majority 
of industrial enterprises. A factory is usually built and 
equipped by means of money which is directly furnished 
by the promoters of the enterprise. It may be that a 
mortgage will be placed upon the buildings and machinery, 
but this will be only a small proportion of the entire capi- 
talization needed to launch the enterprise. On the other 
hand, railroads are built very largely on the proceeds of 
borrowed money, which is secured by bonds of the road. 
Although the amount of nominal capital may be, and 



18 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

generally is, equal to the issue of bonds, the amount of 
paid-in capital is frequently but a very small proportion 
of the bond issues. In the early history of railroading, 
when the whole country was ripe for such work, when 
railroad facilities were very greatly needed, and when com- 
munities became convinced, as was actually true, that 
almost any railroad would ultimately be a paying invest- 
ment, it was generally possible to borrow a very large 
proportion, if not all, of the money required for an enter- 
prise on the basis of the bonds. In theory the capital stock 
of the road should represent the great bulk of its cost, 
and the bond issue, if any, should only represent the debt 
which must be placed on the property after the capital 
is subscribed in order to complete the work, but in this 
country the practice seems to have gone almost to the 
other extreme. Roads are usually bonded to the highest 
possible limit, while the amount of money actually fur- 
nished on capital stock represents the margin between 
the necessary cost and the confidence of the public in the 
enterprise as a whole. 

The English plan of building railroads appears to have 
been very different. The railroad charters were modeled 
largely on the charters of the previously established turn 
pikes. The turnpike companies did not own their roads, 
but merely owned the right to operate them and to charge 
toll for their use. Following this idea, an English railroad 
cannot mortgage its property in the sense in which it can 
be done in this country. They may issue debenture 
bonds, which are merely a lien on the income of the road, 
but which will not permit the road to be sold under fore- 
closure, even if the road should default the payments of 
interest. In this country the mortgage carries with it the 
right to demand the sale of the road, under a certain legal 
form of procedure, if the obligations imposed by the bonds 
are not fulfilled. 



THE ORGANIZATION OF RAILROADS. 19 

9. Charters. — It has been declared that charters are not 
laws, but exemptions from the laws. The term charter, 
as apphed in the time of the Middle Ages, represented a 
special privilege granted by the king to do some act, to 
collect some revenue, or to enjoy certain privileges which 
were not granted to the people in general. When the 
turnpike roads and canals were first authorized, each was 
granted a charter which gave to each company certain 
peculiar rights and privileges. When railroads were first 
constructed, they were authorized by special legislation in 
a somewhat similar manner. To a considerable extent this 
is essential, since the railroads necessarily must be enabled 
to exercise the right of eminent domain. The fact that 
some railroads have been built with little or no difficulty, 
so far as obtaining right-of-way is concerned, the right-of- 
way having been donated, and with extensive tracts of 
lands thrown in as a bonus, does not weaken the general 
statement that a railroad would be helpless unless it were 
enabled to exercise the right of forcing its way wherever 
engineering requirements shall dictate. But as the number 
of railroad projects multiplied, the forms of charters which 
were granted were frequently simplified by referring to 
the terms of a charter which had been previously granted. 
This gradually led to the adoption of general railroad laws, 
which thereby changed the granting of a charter into a 
mere matter of routine procedure instead of a special 
legislative act. The various States have been gradually 
coming into line in this respect, so that roads which are 
constructed in the future will be authorized by a more 
nearly uniform legal procedure. An examination of the 
charters on which the largest railroad systems of the 
present day rest will show a very curious situation with 
respect to many of them. For example, the Northern 
Pacific Railroad, with a mileage of over 5600 miles, is 
operated on the basis of a charter which was granted for 



20 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

the construction of an unimportant line in Wisconsin. 
Even this httle Hne was not built, but the charter was 
slightly amended by the State Legislature, and on the 
basis of this insignificant charter this great system was 
built and is operated. 

10. General railroad laws. — The earlier charters of 
roads usually began with a preamble reciting that there 
was a pubhc necessity for the project. The general rail- 
road laws follow this idea to the extent of requiring the 
promotors of an enterprise to present evidence before a 
railroad commission that the proposed road is a public 
necessity and that it has ^^ sufficient utility to justify the 
taking of private property." Whenever there is any 
limitation regarding railway rates, the limitations have 
usually been placed so high that they have never been 
invoked. Sometimes the Legislature has been empowered 
to reduce rates without the consent of the company, but 
this provision is usually accompanied by the proviso that 
such action shall not be taken if it can be shown that it 
would thereby reduce the net profits of the road below 
some limit, say 10% per annum. Such a hmitation usually 
renders the provision of no effect. Many charters have 
contained the provision that if the net profits of the road 
shall exceed a certain per cent all excess profits of the 
road shall be turned over to the State. It is probably true 
that no State has ever profited in this fashion, since the 
astute railroad manager would see to it that if the profits 
should ever show a tendency to go beyond the limitation^ 
the money would be spent in improvements to the road. 
One of the finest railroads in the country is subject to such 
a limitation. Its excess profits have therefore been spent 
in this fashion, with the result that the added conveniences 
and faciUties have still further increased its business, 
until the road is now one of the most gilt-edged railroad 
properties in the country. 



THE ORGANIZATION OF RAILROADS. 21 

The number of incorporators required varies in the 
different States, only two or three being required in several 
States, while twenty-five are required in some others. The 
minimum amount of capital stock is frequently specified 
as $10,000 per mile of road. An affidavit that some per- 
centage, say 10% of the total capital stock, has actually 
been paid in cash is required in many States. Some 
charters limit the corporate existence to some definite 
period, such as 50 or 99 years. A map which shows 
the line of the road with more or less definiteness must be 
filed with the secretary of state, and it is sometimes 
required that a map showing the route through each 
county must be filed with the county clerk of that county. 
Many other specifications regarding the method of con- 
structing the road, details regarding construction of rolling 
stock, such as safety appliances, the protection of highway 
crossings, etc., are required by the general railroad laws 
of various States. For a brief but comprehensive com- 
pilation of these, the reader is referred to ^'Railway Legis- 
lation in the United States," by Dr. B. H. Meyer. 

II. General railroad law of the State of New York. — 
Some of the principal features of the general railroad law 
of the State of New York are quoted as a sample of one 
of the best and most equitable of such laws. The number 
of railroad incorporators may be fifteen or more. They 
shall file a certificate which shall state the name of the 
corporation; the number of years it is to continue; the 
kind of road; its length and termini; the name of each 
county in which any part is to be located; the amount of 
capital stock (not less than $10,000 per mile or, with 
narrow gauge, $3000), and the number of shares of stock. 
If the capital stock is to consist .of common and preferred 
stock, the rights and privileges of the preferred stock over 
the common stock must be clearly stated. It must have 
at least nine directors, and the name and post-office address 



22 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

of each of the incorporators, with the number of shares 
of stock to which he subscribes, must be stated. One of 
the most important provisions against irresponsible proj- 
ects is that an affidavit must be made by at least three of 
the directors that at least 10% of the minimum amount 
of capital stock required by law has been subscribed and 
paid in cash. A railroad corporation, after being duly 
organized, has the power to enter upon any lands in order 
to make any necessary surveys, but is subject to liability 
to the owner for all damage done; it is also authorized 
to acquire property which may be needed, and, if necessary, 
to acquire such property by condemnation proceedings. 
It may construct the road across, along, or upon any 
stream, watercourse, highway, plank road, turnpike, or 
across any of the canals of the State which the route of 
its road shall intersect or touch. This last provision, as 
well as the other provisions here given, is subject to 
modifications by special laws- which apply particularly to 
the crossing of highways and canals. It may make a 
junction with any railroad which it may reach or cross, 
and may even compel, if necessary, the connecting road 
to allow suitable turnouts, sidings, and switches to be put 
in. The corporation may ''take and convey passengers 
and property on its railroad by the power or force of steam 
or of animals or by any mechanical power, except where 
such power is specially prescribed in this chapter, and to 
receive compensation therefor." This virtually means 
that roads of any kind, whether the cars are propelled by 
steam, electricity, or even horse-power, are authorized to 
convey '^persons and property" which includes freight. 
This disposes of the question of the authority of electric 
roads to carry freight, which is the subject of contention 
and legislation in other States. The corporation is also 
authorized to borrow money and to issue bonds for its 
security without any definite limitation of the amount, 



THE ORGANIZATION OF RAILROADS. 23 

except that such a measure must have the consent of the 
State Board of Railroad Commissioners and of the stock- 
holders owning at least two-thirds of the stock. Work 
must be begun within five years, and during that time at 
least 10% of the amount of capital must be expended. If 
the road is not finished and put in operation within ten 
years from the time of filing the certificate of incorpora- 
tion its corporate existence and powers shall cease. The 
corporation is required to make a map and profile of the 
road adopted by it in each county through which it passes, 
and file a copy in the office of the county clerk. Written 
notice must be given to the actual occupants or owners of 
the lands over which it passes regarding the time and 
place of fifing the map and profile. Such occupant or 
owner may within fifteen days give a ten days' written 
notice of an application to a Justice of the Supreme Court. 
The Justice may appoint three disinterested persons, one 
of whom must be a practical civil engineer, who shall pass 
upon the question of a proposed alteration in the line. 
The law is quite elaborate regarding the hearing of any 
plea for a proposed alteration of the line, with rules regard- 
ing appeals, etc. The maps filed with the railroad com- 
mission must show "length and direction of each straight 
line; the length and radius of each curve; the point of 
crossing of each town and county line, and the length of 
line of each town and county accurately determined by 
measurements to be taken after the completion of the 
road." Changes of route from the original route selected 
may be permitted under several elaborate regulations. 

There are numerous physical requirements regarding 
construction, operation, and management of the road, of 
which a few of the most important are as follows: On 
narrow-gauge roads the weight of the rail must not be 
less than 25 pounds per yard; on standard-gauge roads it 
must be not less than 56 pounds per yard on grades of 



24 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

110 feet to the mile or under, and must be at least 70 
pounds per yard on steeper grades. Fences must be 
erected as soon as the land is appropriated for use. Cattle- 
guards must be provided. If the fences are not made or 
are not kept in good repair the corporation is liable for 
damages to domestic animals, but when they are kept in 
good repair the corporation is not considered liable for 
damages unless ^^negligently or willfully done." Barbed 
wire, however, is not permitted for fence construction. 
The railroad need not be fenced when it is not necessary 
to prevent horses, cattle, sheep, and hogs from going upon 
its track from the adjoining lands. Farm crossings must 
be maintained wherever necessary. Sign-boards of such 
shape and design as are approved by the Board of Railroad 
Commissioners must be placed at all grade crossings. The 
Supreme Court or the County Court may upon action 
require a railroad to station flagmen or even to erect, 
maintain, and operate crossing gates at any highway 
grade crossing. No station which has been established 
by the railroad shall be discontinued without the consent 
of the Board of Railroad Commissioners. All railroads 
crossing another railroad at grade must bring all trains to 
a full stop between 200 and 800 feet from the crossing, 
and then shall cross only when the way is clear and upon 
a signal from a watchman stationed at the crossing. If 
two railroads cannot agree as to expenses the matter will 
be decided by the Supreme Court. The full stop may be 
omitted with the approval of the Commissioners if inter- 
locking switch and signal apparatus has been adopted. 
For ordinary steam railroads the permissible passenger fare 
is 3 c. per mile, with a right to a minimum single fare of not 
less than 5 c. The Legislature reserves the right to reduce 
fares, but cannot do so without the consent of the corpora- 
tion, if it may be shown that the net profits would be less 
than 10% per annum on the capital actually expended. 



CHAPTER III. 

CAPITALIZATION. 

12. Stock. — The total railway capitalof the roads of 
the country, as reported to the Interstate Commerce Com- 
mission for the year ending June 30, 1904, aggregated 
$13,213,142,679. This capitahzation was at the average 
rate of $64,265 per mile. The capitalization represented 
stock to the amount of $6,339,899,329, which is 47.98% 
of the total capitalization. This is slightly less than the 
percentage in previous years, although during the last 
eleven years this percentage has only varied from 47.44 
to 50.87%. The average amount of stock per mile of hne 
for that year was $30,836. This value has been singularly 
uniform for many years past in spite of the large increase 
in the mileage. This total issue of stock is divided into 
common and preferred stock, of which the preferred stock 
for the year given was $1,289,369,860, which was a little 
over 20% of the total. Preferred stock usually carries the 
right to a dividend at a fixed percentage, which dividend 
must be paid before any dividend can be declared on the 
common stock. Frequently, although not always, these 
dividends are cumulative, which means that if for a period 
of one or more years the railroad is unable to pay them, 
the defaulted dividends constitute a lien on the road 
which must be paid ultimately before dividends may be 
paid on the common stock. This stock therefore occupies 
an intermediate place between a bond and the common 
stock. It carries with it no authorization to foreclose and 

23 



26 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

sell the road in order to secure a payment of either prin- 
cipal or interest, but, on the other hand, the interest or 
dividends, although definitely limited in amount, have a 
priority over the payment of any dividends on the conmion 
stock. 

Although the capital stock per mile of line for the whole 
United States has been singularly uniform for a long 
period of years, which shows a uniformity in practice from 
year to year, there is a considerable variation, as might 
have been expected, in the capital stock per mile of line 
for railroads in the various groups. For example, the 
capital stock per mile of road in Group II, which includes 
.New York, Pennsylvania, New Jersey, Delaware, and 
Maryland, is over $62,000 per mile. On the other hand, 
in Groups V and IX, which include the Gulf States, together 
with Kentucky and Tennessee, the capital stock is less 
than $20,000 per mile. This is only what might have been 
expected, considering the relative general wealth of the 
two sections. The percentage of the capital stock to the 
total capitalization, however, remains more nearly uni- 
form. The lowest percentages are likewise in Groups V 
and IX. This indicates that although as a matter of 
fact the total capitalization per mile of road is less in 
these two groups than in any others, the issues of capital 
stock are a far less proportion of the total capitalization, 
and that the roads have been built chiefly on the capital 
obtained from the issue of bonds, probably subscribed 
more largely by non-residents. Although nearly the same 
disparity is shown in these two groups, and especially so 
for Group IX (Texas and Louisiana), regarding a low issue 
in bonds per mile of road, the percentage of the bond 
issue to the total capital is practically normal for these 
two groups. 

13. Funded debt. — The total funded debt, which usually 
is about 50% of the total capitalization, consists of ordinary 



CAPITALIZATION. 



27 




28 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

bonds, income bonds, equipment trust obligations, and 
miscellaneous obligations. An income bond is practically 
the same as preferred stock with cumulative dividends. 
They are issued only after ordinary bonds have been issued 
to as great an extent as is considered financially safe. The 
interest on these bonds is only payable after the interest on 
prior bonds has already been provided for. 

Another type of bond which is frequently used during 
the reorganization of a bankrupt property is called a 
convertible bond. Such bonds carry a provision at some 
definite basis for their conversion into stock at the option 
of the holder. 

Equipment trust bonds are really chattel mortgages 
"which are issued to pay for unusual expenditures in new 
equipment. Since the property which constitutes the 
security of such a mortgage has a short hfe and will un- 
doubtedly become practically worthless in a comparatively 
short term of years, such bonds contain provision for a 
sinking-fund by which the principal will be returned 
in annual installments and become entirel}^ repaid 
within the estimated period of the physical hfe of the 
equipment. 

All of these special forms of bonds constitute about 
20% of the total bonded indebtedness. The great bulk of 
the bonded indebtedness consists of the ordinary form of 
bond with a definite rate of interest and with the provision 
that, if the interest is not promptly paid, the holders of 
the bonds may apply to a court for the appointment of a 
receiver, who will be authorized to administer the road 
if it is considered possible that a new management might 
succeed in rendering the property financially solvent, or 
else to arrange for th^ sale of the road under foreclosure. 
A foreclosure sale may be ordered not only for the failure 
of the road to pay the principal at maturity, but also for 
failure to pay the interest when it is due. The law varies 



CAPITALIZATION. 29 

somewhat regarding the rights of bondholders, but usu- 
ally a very small proportion of them, even one-tenth, may 
institute foreclosure proceedings. 

14. Dividends on stock. — A very brief investigation of 
the records of railroad stock will show that it is a very 
precarious form of investment. It is unfortunately true 
that but very few roads which are old enough to have a 
history have escaped a receivership, or at least a period 
in which no dividends were paid. Many stockholders have 
considered themselves lucky that their stock has not been 
altogether wiped out by a foreclosure sale. On the other 
hand, the returns on the stocks of some roads have been 
phenomenally large. Frequently a road will commence 
business by calling for a payment of 10% on its stock. 
As the demand for money increases and the credit of the 
enterprise diminishes by the issue of bonds until no more 
bonds will be taken up, the stockholders will be called on 
for larger payments on their stock-subscriptions. In 
many cases where the road is successful from the start 
and its prospects have been so great that a large propor- 
tion, if not all, of the cost of construction and initial 
operation have been obtained from the proceeds of the 
sale of bonds, the stockholders begin to earn dividends 
when they have only paid 10 or 20% of their stock. In 
the improbable case that the road is able to maintain such 
a record, a regular dividend of 6% on the par value would 
mean virtually a dividend of 60% (or 30%) on the amount 
actually paid in. But in spite of the very favorable show- 
ings made on some roads, the statistics show that a large 
proportion of railroad stock actually pays no cUvidends. 
During the depression following the panic year of 1893, 
there was a period of three years in which 70% of all the 
railroad stock of the country paid no dividends whatever. 
It is useless to minimize this statement by saying that 
much of railroad stock has been '^watered." If a road 



30 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

pays no dividends, the original bona-fide payments for 
stock, as well as the ^^ water " in the stock, get no return 
on the investment, and for that period of three years 70% 
0f railroad stock paid no dividends. The 30% which suc- 
ceeded in paying dividends only paid them at an average 
rate of about 5.6%. Since that time the situation has 
grown far better.' The percentage of stock which pays no 




wM/////m///m////m///M////W^^ 



1888 9 ■ 1890 123 .156789 1900 1 2 

Fig. 5. — Percentage of stocks paying no dividends. 

dividends has been reduced to about 42%, and yet the 
last few years have been the most prosperous years known 
in railroad history. There is some mitigation of the above 
gloomy view when we consider that a large proportion, if 
not the total, of the stock of many small branch railroads 
is owned by the larger trunk lines, with which they connect, 
in their corporate capacity. The larger railroads utihze 
these smaller roads as feeders which add to the earnings 
of the main hne. Even though the earnings directly 
assigRable to the branch line are not sufficient to earn 
more than enough to pay the operating expenses and the 



CAPITALIZATION. 31 

interest on the bonds, the larger raihoad company as 
owner is securing a return on its investment, in the 
indirect form of through-business furnished to its main 
Une, which adds to the receipts of the main hne far more 
than the added business costs. The fact that about 30% 
of all railroad stocks outstanding are owned by railways 
in their corporate capacity, and that some of it brings an 
indirect, if not direct, return, materially modifies the above 
statement regarding stocks which do not pay dividends. 

If we analyze the situation with respect to different 
sections of the country, we find a very marked differ- 
ence. Group VII, comprising the region between the 
Rocky Mountains and the Missouri River, has the best 
record regarding roads which failed to declare divi- 
dends, less than 8.5% having failed to do so. Over 
40% of the stock in that group paid from 7 to 8 per cent. 
The largest amount of stock belongs to Group II; in this 
group a large percentage paid from 4 to 8 per cent. The 
Pacific States, Group X, are erratic, over 80% paying no 
dividends while 1J% paid over 10%. 

15. Interest on bonds.^The record of the payment of 
interest on bonds is of necessity far better than that of 
paying dividends on stock. Excluding equipment trust 
obligations from consideration, less than 4J% of the 
bonds defaulted their interest. Although the very large 
bulk of bonds pay from 3 to 6% interest, there is a con- 
siderable percentage which pays 7 or 8% and even a little 
over. ' Considering the railroads of the United States as 
one system (and thus ehminating the intercorporate pay- 
ments made to a railroad which owns the bonds of another 
road), the net interest on the funded debt for 1903 and 
1904 required a httle over 14% of the gross earnings from 
operation. Even this figure is a considerable reduction 
from the corresponding figures for previous j^ears, owing 
largely to the general policy of refunding railroad secur- 



32 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

ities at a lower rate of interest. Although there is a very 
large variation in individual cases of the proportion of 
gross earnings which must be paid out for interest on the 
funded debt, it is remarkable that such a large percentage 
of all railroads expend nearly the same proportion of their 
gross earnings in this way. This uniformity seems to be 
regardless of the length of the road, except that, the larger 
the system, the greater the probabihty that the average 
figure will be approached. The largest variations from 
average figures occur with very small branch fines which 
are operated under special operating conditions and 
financial agreements. 

1 6. Taxes. — The item of taxes is usually included under 
fixed charges. For the year ending June 30, 1904, the 
total amount paid in taxes by the railroads of the United 
States amounted to $61,658,373. Of this amount $1,324,- 
808 was paid upon property owned by railroad corpora- 
tions but not used in operation. If we deduct this from 
the total, we have, as the amount of this expense assigned 
to operation, $60,333,565. The commercial valuation of 
railroad property as given by the Bureau of the Census 
was $11,244,852,000. Upon this basis the average rate of 
taxation would amount to about $5.37 per thousand. The 
basis of the assessment of these taxes is somewhat variable, 
although over 70% is assessed on what is considered to 
be '' the value of real and personal property." About 10% 
more of the tax was computed on the basis of the market 
value of the stocks and bonds or on a valuation of the road, 
which is based on the actual earnings, dividends, or other 
results of operation. In ah States and Territories of the 
Union the first system is used, but in some States a second 
system is employed to supplement the first. In addition 
to the above systems, which may be called ad- valorem 
taxes, about 18% of the taxes collected were based on some 
special system of taxation, such as a tax on the gross or 



CAPITALIZATION. 33 

net earnings, revenue, or dividends. Sometimes a tax is 
paid on the amount of traffic, or on some physical prop- 
erty of the road operated, or on some special privilege 
which has been granted. Sometimes there is a special 
taxation on stocks, bonds, loans, etc. 

The amount of these taxes per mile of line of course 
depends chiefly upon the actual valuation of the road per 
mile, but it also depends upon the system of taxation in 
the various States and Territories. In the State of Massa- 
chusetts, where the valuation of the railroad per mile of 
line is very high, we would expect a high tax-rate per mile, 
but it is apparently far higher on the basis of actual 
valuation than in other States, since it amounts to $1426 
per mile. Connecticut comes next with $1114 per mile. 
In the State of New Jersey, where the actual valuation of 
the railroads is nearly, if not quite, as high as in any other 
State, the amount of taxes per mile of line is $798, while 
in New York and Pennsylvania it is $581 and $482 
respectively. In some of the Southern States, where the 
valuation of the railroads per mile of Hne is comparatively 
low, we find, as might be expected, a low tax-rate per 
mile, that in Florida being $150 and in Alabama $182. 
In Texas the rate is only $110, and in Indian Territory it 
amounts to only $19. The average for the whole United 
States is $301 per mile. 

17. Small margin between profit and loss. — The gross 
revenue received by a railroad is applied first to the 
payment of operating expenses. As an average for the 
whole United States this amounts to approximately 65%. 
From the remainder must be paid the interest on the funded 
debt and current liabilities, and also the taxes. , This will 
take about 20% more, but it is not even permitted to 
use all of the remainder for dividends, since a very large 
fund is needed for permanent improvements and for 
bolstering up weak branch hnes which are not paying 



34 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

their expenses but which are operated because of their 
indirect or their future value. It will thus be seen that 
the dividends are only paid out of the last small percentage 
of the gross earnings. Since there is so much variation 
in the financial condition of railroads, from one which 
is unable to pay its operating expenses to another which 
is declaring dividends on watered stock, we may learn 
something by studying the statistics of all the railroads of 
the United States ^' considered as a system." This last phrase 
refers to the fact that, since such a considerable proportion 
of railway stock is held by railway companies in their 
corporate capacity, there is a very large percentage of 
payments made to and by railroad companies which are 
merely intercorporate payments. By deducting those 
payments, which would appear as receipts in the accounts 
of one road and as expenses in the accounts of another, 
we may prepare a statement such as would be made up 
if all the railroads of the country were actually combined 
into one system. Another condition which somewhat 
comphcates the situation is due to the fact that railroads 
are also the owners of property which brings in an income 
totally independent of their work as common carriers. 
In 1904 this ^^ clear income from investments" amounted 
to nearly $50,000,000, although it was only 2i% of the 
gross earnings, but such income has been ignored in the 
following statements. The table on page 35 gives the gross 
earnings of the railroads of the country considered as one 
system for the year ending June 30, 1904 (using even 
milHons throughout). 

The actual amount of surplus available for "adjustment 
and improvements" was nearly $50,000,000 in excess of the 
$94,000,000 surplus gi venin the table, on account of the added 
sources of income not included in " gross earnings from opera- 
tion." It should be noted that in the above case the divi- 
dends were taken from the last 9.3% of the gross earnings. 



CAPITALIZATION. 35 

Earnings from passenger service $ 444,000,000 

" freight " 1,379,000,000 

'' '' other sources 152,000,000 

Gross earnings from operation $1,975,000,000 

Subtracting operating expenses 1,339,000,000 

We have as net earnings 636,000,000 

Out of these earnings were paid, 

Taxes $ 62,000,000 

Interest on debt and on current lia- 
bilities 296,000,000 

and then dividends 184,000,000 542,000,000 

leaving a surplus of 94,000,000 

The dividends actually paid averaged less than 3% on 
the total capital stock. That which has been called 
surplus may almost be considered in the light of an expense, 
since it was not considered wise to increase the dividends 
beyond the amount actually paid. The average revenue 
per passenger per mile amounted to 2.006 c. The revenue 
per ton of freight per mile amounted to .780 c. If the 
passenger and freight receipts, as well as the rates on 
mail, express, etc., had been cut down 10% without any 
increase in business the amount available for dividends 
would have been entirely wiped out. Even cutting them 
down 5% under the same conditions would have cut 
the dividends in two. It may thus be readily seen that 
there is but a small margin between large dividends and 
no dividends, which will be produced by comparatively 
small differences in rates. 

Of course the above should not be interpreted as meaning 
that a difference in the amount of business done will have 
the same effect on dividends. Although to a very con- 
siderable extent it is true that when times are hard and 
business is slack, so that the amount of traffic is reduced, 
the gross expenses of the railroads are cut down, they 
cannot be cut down in strict proportion to the reduction 



36 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

in traffic. It will be shown later on that the cost of 
running an extra train is by no means equal to the average 
cost of running all trains. To put it more concretely a 
railroad which is regularly running 20 trains per day 
each way can run one additional train per day each way 
for much less than 2V of the average cost. Vice versa, 
the saving which is made by running one less train, because 
the traffic has been cut down, is less than /^ of the average 
cost. If, therefore, a road is doing a certain gross amount 
of business which requires say 20 trains per day, a 
change of policy which increases or diminishes the amount 
of business done will increase or diminish the gross receipts 
in strict proportion to the change in the business, but 
the change in operating expenses will be far less. If the 
business is reduced say 10%, the gross receipts are 
reduced 10%, while the operating expenses are reduced 
probably not more than 4 or 5%, and the probable result 
is that all money which otherwise might be devoted to 
dividends has been entirely wiped out. On the other 
hand, an increase in business of 10% will not increase the 
operating expenses more than 4 or 5%, and therefore 
the amount for dividends may be nearly doubled. This 
fact may be made still clearer by a concrete example. 

18. Variation in dividends due to small variations in 
business done. — Assume that by changes in the alinement 
the business obtained has been increased or diminished 
10%. Assume that the operating expenses are 67% of 
the gross receipts. Assume that the amount required for 
taxes, for the interest on the bonds, and for such demands 
for permanent improvements, working capital, etc., as 
are considered essential before dividends can be paid^ 
amount to 28%. We will have a balance left of 5% 
available for dividends. Assume a change of policy by 
which a 10% increase of business is obtained. As an 
approximate figure we may say that this additional 



CAPITALIZATION. 



37 



business may be carried at a cost of 40% of the average 
cost of the traffic. We will also assume that the reduc- 
tion of 10% in traffic reduces the expenses by a similar 
amount. The comparative effect may therefore be stated 
as follows: 





Business increased 10%. 


Business decreased 10%. 


Operating exp. = 67 
Fixed charges, 

etc = 28 


67[1 + (10%X40%) =69.68 
= 28 . 00 


67[1-(10%X40%)] 

Income 

Deficit 


= 64.32 
= 28 . 00 








95 

Total income 100 


97.68 
Income 110.00 


92.32 
..90.00 


Available for divi- 
dends 5 


Available for divi- 
dends 12.32 


. 2.32 



The above comparison is useful chiefly to indicate a 
principle rather than as a computation of definite value. 
It indicates in one case that an increase in business which 
may be obtained perhaps by mere changes in manage- 
ment more than doubles the amount available for dividends. 
On the other hand, a decrease in business, which may be 
due solely to poor business management, not only wipes 
out a dividend but actually creates a deficit . The numerical 
accuracy of the calculations of course depends on the 
estimate that the additional business only increases the 
cost for handling by 40% of the average cost. While 
the cost of running additional trains will be more than 
40% of the average cost per train-mile, the cost of running 
additional cars in a train, which is not actually limited 
by grade, will be far less than the proportional cost of 
an additional train. The additional cost is still less when 
the manager secures traffic to move in the direction in 
which the traffic is ordinarily least. It is still less when 
the freight is carried in cars which would otherwise return 
empty. In fact under the last condition the added 
receipts are almost pure profit and the additional cost is 



38 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

SO insignificant that it might almost be neglected. There- 
fore the estimate of 40%, as used in the above calculation, 
might be considered as a conservative average. If the 
increase in business can only be obtained by an increased 
expenditure which will make a permanent addition to 
the fixed charges, the above method of calculation will 
show whether the improvement is justifiable. The 
accuracy of the calculations will then depend on the 
accuracy v/ith which the future increase of business may 
be predicted, but if the increase in receipts is greater 
than the addition to the fixed charges, and particularly 
if it is very much greater, there can be but little question 
as to the value of the proposed improvement. 

19. Practical limitations of capitalization. — Theoretic- 
ally there is a definite limit to the proper capitalization 
of every railroad project. Even if it is possible to obtain 
from a credulous public more capital (in the form of 
bonds) than the project requires, the effect is to burden 
the road with unnecessary "fixed charges" for bond 
interest. If more stock is subscribed for and paid in 
than can profitably be used, the usual result is wasteful 
expenditure, and the inevitable result is a decrease in the 
rate of dividends. In either case the credit of the road 
is impaired by the reduction in net earnings. The result 
of the over-capitalization may be actually financial 
embarrassment. 

The other extreme is far more common. The project 
may fail to attract the capital necessary to build the 
road properly and to operate it until its normal traffic 
income is being regularly obtained. If the obtainable 
capital is exhausted before the road is put in operation 
the loss to the projectors is very great and is sometimes 
nearly or quite total. In anticipation of such a predica- 
ment a road is sometimes opened for traffic, using rails 
or ties which are too light, using little or no ballast, uncom- 



CAPITALIZATION. 39 

pletecl earthwork having narrow cuts and no ditches 
and very narrow embankments, and many other devices 
for reducing the cost of the road before traffic-trains are 
run. To some extent such measures are justifiable, but 
it should always be remembered that it is frequently 
very expensive '^ economy" and that the operating expenses 
are thereby increased — often to such an extent as to wipe 
out an easily obtainable profit. Although it is unfor- 
tunately true that the engineer of the road must make 
the best of the capital which is furnished him for the 
work, be it great or small, yet the recommendations of 
the engineer should largely control the efforts to secure 
capital. The engineer should be competent to recommend 
how much capital may profitably be spent to secure the 
greatest rate of net return on the capital invested. 

20. Principles which should govern the amount of capi- 
tal to be raised. — (1) The project should secure sufficient 
capital to insure the proper completion of the road and 
its operation until the normal traffic income is obtained. 
An estimate of this amount can readily be made and the 
projectors should not be satisfied with anything less. 
It might even be stated more strongly to say that the 
projectors are foolish to embark on the enterprise unless 
they have a reasonable certainty of raising this amount. 

(2) The surveys may develop the fact that some addi- 
tional expenditure may permit an improvement on the 
line as originally laid out. An illustration of this (elabor- 
ated in Chapter XV) is the reduction of the rate of the 
ruling grade, which is shown to have a definite financial 
value. The criterion in such a case is this: If the im- 
provement is unquestionably justifiable, on the basis of a 
reasonable capitalization of the annual saving in operating 
expenses, then the improvement should be made, unless 
there is danger that the total available capital is limited 
and that the whole enterprise may become imperiled by 



40 THE ECONOMICS OF RAILROAD CONSTRUCTION, 

an expenditure which is not absolutely essential even 
though desirable. 

(3) In considering such a case as the above, the pos- 
sibihty of merely deferring the extra expenditure without 
ultimately abandoning work already done must be con- 
sidered. In some cases the plan as actually constructed 
becomes practically a finality, which cannot be changed 
except at prohibitive loss. Under such conditions the 
best plan (from the operating standpoint) must be insisted 
on. 

(4) On the other hand, no change or "improvement" 
should be adopted, unless it can be demonstrated that 
the change itself will be financially justifiable. It is not 
sufficient that its cost will not wreck the enterprise. 

(5) The engineer can usually count on the fact that 
unless the money market is abnormally disturbed by 
panic conditions any enterprise which is really meri- 
torious can command sufficient capital to float it, if it 
is properly exploited. Even an improvement to the 
original plan can command capital if it has sufficient 
merit, although this may be more difficult than to raise 
the original sum asked for. 



CHAPTER IV. 

THE VALUATION OF RAILWAY PROPERTY. 

21. Objects. — There are several objects for which a 
valuation is placed on railway property. The method of 
making the valuation as well as the value arrived at is 
apt to depend very largely on the purpose for which it is 
made. An estimate may be made for the purpose of 
taxation. Another and very different estimate may be 
made by the agents of individuals or a corporation who 
are contemplating buying the property. Legislatures 
may wish to obtain a valuation which may be used as a 
basis for some form of railroad legislation. The fact that 
some railroad properties have become very valuable and 
have returned very large profits to their promoters has 
caused a general behef throughout the country that 
railroad earnings are far higher than a fair return on 
their valuation will justify. This has resulted in the 
demand that railway-rates should be reduced so that 
the net earnings will be more nearly in proportion to 
the true valuation of the road. Some of the methods of 
appraising railroad property will be here discussed. 

22. Nominal valuation.^The nominal valuation of a 
railroad property is the sum of the par values of its stocks 
and bonds. On the basis that a bond is a mere evidence 
of indebtedness and that it represents money which has 
been used to create the property, the bondholder may 
be considered as one of the owners of the road and that 

41 



42 THE ECONOMICS OF RAILKOAD CONSTRUCTION. 

his rights and control of the property are merely some- 
what different from those of a stockholder. If the capital 
stock is not fully paid, then of course the true valuation 
must be considered as the sum of the paid-in capital 
together with the bonds and other liabilities. Of course 
such figures are very approximate and are discussed 
chiefly on account of their simpUcity. When the road 
is first constructed, such figures ought to be a fair repre- 
sentation of the value of the physical property, provided 
expenditures have been cautiously and efficiently made. 
Such a valuation does not assign any value to the fran- 
chise or the charter of the road. A railroad property is 
very different from any other form of landed property. 
A tract of land, averaging about four rods in width 
and an indefinite number of miles in length, is di- 
verted from its original use as farmland or other pur- 
poses and devoted to a particular use. A very large 
amount of money is spent in grading, in the construction 
of tunnels and the building of bridges, and the construction 
of the road-bed and track. Except for the comparatively 
insignificant value of the rails, which may be torn up 
and sold as second-hand rails, or the value of steel bridges, 
which may be removed and erected elsewhere or sold 
for scrap, all the money which is spent for ^he construc- 
tion of the road is absolutely sunk beyond hope of recla- 
mation. It can only be used for one purpose, and the 
value of the property as an investment is represented 
by its earning capacity when used for its one sole purpose 
of being a common carrier. Thereafter its value is really 
represented, not by the amount of money which has been 
sunk in the enterprise, but by the capitahzed value of 
the road as an organization for earning money in one par- 
ticular way — that of a '^ common carrier." If the road 
is well located for obtaining business, which is virtually 
the same as saying that it has a valuable franchise, then 



THE VALUATION OF RAILWAY PROPERTY. 43 

it will probably earn dividends on a comparatively small 
expenditure of capital. On the other hand, if there is 
but little business to be done, its earnings will be small, 
no matter how much the road may have cost. We may 
thus see that the amount which has been spent on the 
construction of the road does not necessarily bear any 
relation to the real value of the railroad property. Prac- 
tically the two values will ordinarily approach equality. 
If the amount of money which has been spent is far 
higher than is justified by its earning capacity, it simply 
indicates that the expenditure has been foolishly made. 
If, on the other hand, it is far less, then it means that 
the promoters have seized an unusual golden opportunity. 
It would seem unnecessary to point out any further 
fallacies in the method of valuation from the amount 
of money spent in construction, if it were not for the 
fact that so many people still chng to some such method. 
Such a method sometimes gives values which are far too 
great, while in other cases they are far too small. To 
quote from one writer on the subject: ^'The commercial 
value has nothing to do with its cost. If John Smith 
buys a hotel for $1,000,000 and, although a good hotel 
man, cannot make more than $50,000 a year out of it, 
and wants to sell, the commercial value is probably not 
over $500,000." A hotel man might go into a wilderness, 
select a site for a hotel on land which costs him practically 
nothing, build a summer resort at a comparatively small 
expenditure, and in a few years create a custom and 
give his hotel a name and reputation which would make 
his hotel property exceedingly valuable and worth many 
times its original cost. Under such conditions, the 
market value of that hotel would have little or no rela- 
tion to its actual cost. 

23. Cost-of-replacing-property method. — There is a large 
class of people who think that a road should be valued 



44 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

according to the cost of replacing the property at the 
present time, i.e., buying the right-of-way, constructing 
the road-bed and track, and providing its equipment. 
There are several causes which will operate to make such 
a valuation very unfair. Such a valuation takes no 
account whatsoever of the earning capacity of the road. 
A railroad may be so well located that its annual 
earnings are very large, so large that the pubHc values 
its stocks and bonds, as quoted in the stock-market, 
at a very high figure, and yet the cost of duplicating that 
road in every particular at present-day prices might be 
very much less than the market price of its securities. 
As another reason, it is almost invariably found that 
-any business enterprise, whether it is a factory or a rail- 
road, which has been in existence for a series of years 
long enough for a considerable part of its construc- 
tion to have been renewed by methods which were not 
in vogue when the structure was originally built, has 
had a total amount of money spent on it which is 
very far in excess of the amount which would replace 
it at the present day. It would certainly be unfair to 
say that, because a railroad-cut, for example, which was 
originally dug out by hand labor at a high price per 
cubic yard could now be taken out with steam-shovel 
methods at one-half the cost, therefore those who had 
paid the high prices for the original work should now 
have the railroad earnings scaled down until they give 
merely a return on the cheapened method of construction 
This method is usually advocated by those who wish * > 
make it a basis for radical legislation which shall reduce 
railroad charges until they merely pay the cost of opera- 
tion plus a comparatively insignificant return on what 
it would cost under present methods to reconstruct the 
road. Such methods seem to lose sight entirely of the 
fact that the element of risk in railroad construction is 



THE VALUATION OF llAILWAY PROPERTY. 45 

very great, and that, as given in a previous chapter, a 
very large proportion of railroad stock pays absolutely 
no dividends. Therefore it is but just that the permissible 
earnings of railroads should be made high enough to 
compensate for the great risk which is run by capitaHsts 
who build railroads. 

24. Valuation of physical properties and franchise. — In 
Michigan and Wisconsin the railroads of the State have 
all been valued by a corps of engineers, appointed by the 
State, who adopted a systematized method of making an 
actual valuation of the property as it exists. Of course 
the method was largely an estimate of the cost of repro- 
duction, allowance being made, however, in those elements 
such as rails, etc., which are subject to wear and deprecia- 
tion, for the ''present value." The various elements of 
cost of a road were classified, and those elements which 
were subject to depreciation were examined particularly, 
while making the appraisal, to determine their present 
value. For the railroads of Michigan, the total cost of 
reproduction of construction and equipment was given as 
$202,716,262, while the present value was given as only 
$166,398,156, or 81.4% of the value when new. Switch- 
ties and cross-ties were allowed a present value of only 
53.9% of the cost of reproduction. Telegraphs and 
telephones were allowed only 52%, while, on the other 
hand, right-of-way, real estate, and grading were allowed 
their full value, 100%. Although this work was under- 
taken by the State with the idea of furnishing a basis for 
a more uniform system of taxation, ''it very soon became 
necessary to publish an order excluding all thought of 
taxation in connection with the results to be obtained." 
"The commissioners required of us only the cost of repro- 
duction and the present value of this road, reserving to 
themselves any adjustments of these values that might 
be thought necessary to secure uniformity of taxation." 



46 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

There was added to the '^ present value" of these proper- 
ties the sum of $35,814,043 as the value of the ''non- 
physical" properties. The non-physical property is sup- 
posed to include among other things the following: 

^'1. It includes the franchise 

" (a) To be a corporation. 

" (6) To use pubhc property and employ pubhc author- 
ity for corporate ends. 

"2. It includes the possession of traffic not exposed to 
competition, as, for example, local traffic. 

^'3. It includes the possession of traffic held by estab- 
lished connections, although exposed to competition, as, for 
example, through-traffic that is secured because the fine 
in question is a link in a through-route. 

"4. It includes the benefit of economies made possible 
by increased density of traffic. 

''5. It includes a value on account of the organization 
and vitafity of the industries served by the corporation, as 
well as the organization and vitafity of the industry which 
renders the service; this value consequently is, in part, 
of the nature of an unearned increment to the corporation." 
(Prom report of Professor Henry C. Adams.) 

The value of the non-physical properties was obtained 
by deducting from the gross earnings from operation the 
operating expenses, exclusive of taxes, which gives the 
net income from operation. Adding to this the net income 
from corporate investments would give the total available 
corporate income. From this is deducted an annuity, 
based at 4% of the mean value of the physical elements, 
which then gives the remainder available for other pur- 
poses. Prom this was deducted further the taxes on the 
physical elements at 1% of their mean value, also the 
rentals on property not covered by the appraisal, also 
the interest on current fiabilities, and also the cost of 
permanent improvements which were charged to income. 



THE VALUATION OF RAILWAY PROPERTY. 47 

Subtracting these deductions from the remainder obtained 
above, we have a surplus (or deficit) which is capitaUzed 
at 7%. This gives such a value of the non-ph)^sical ele- 
ments that it yields a net income of 6% after the payment 
of taxes of 1%. It is a very curious coincidence that 
when the value of the non-physical properties of the 
railroads of Michigan, as it was actually computed accord- 
ing to the above method, was added to the ^'present 
value," the sum total agreed with the cost of reproduc- 
tion to within a quarter of 1%. It is probable, however, 
that this should be considered as a coincidence rather 
than as an illustration of a general law. 

25. Stock-market valuation. — A far more accurate 
method of valuation is to determine the average market 
value of the stocks and bonds of the road for a period of 
time which is long enough to cover the speculative fluc- 
tuations of the stock-market. There is one very strong 
reason for considering this as a true valuation. The market 
price for railroad securities is determined as a compromise 
between two opposing classes of financiers, one of which 
is interested in raising the price as high as possible, 
the other in making it as low as possible. Such men 
are experts in valuation. They make it their life-long 
business. The compromise value which is offered and 
accepted between these two classes of experts may 
therefore be considered as the true valuation of the 
property, provided we can succeed in eliminating from 
the price the effect of fluctuations due to speculative excite- 
ment. The combined value of these securities (stocks and 
bonds) represents the value placed upon the earning 
capacity of the railroad. 

26. Valuation by capitalizing the net earnings. — This 
method requires two steps: the determination of, first, 
the income to be capitahzed, second, the rate of capitaliza- 
tion. The determination of the income to be capitalized is 



48 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

not very difficult, although it requires some modification 
from the ^'net earnings" as reported by the railroad 
companies, with which it should be identical. The diffi- 
culty arises from the variation in the methods of railroad 
companies, in keeping their accounts. The net earnings 
represent the difference between the gross earnings and 
the amount properly assignable to operating expenses. 
For the purpose of this investigation such taxes as are 
paid are allowed as operating expenses so that the remainder 
represents the total which can be applied as a return in 
whatever form to the capital which has been invested. 
The chief difficulty lies in the variation among railroad 
accountants in charging expenditures for permanent 
improvements. One company may purchase additional 
rolling-stock and charge the entire cost to operating 
expenses. Others will charge the entire sum to the 
capital account. If the new equipment is partially to 
replace old and antiquated equipment, some will adopt 
the plan of charging the value of the replaced cars or 
locomotives to operating expenses and charge the remainder 
to the capital account. The last method is undoubtedly 
the correct method to adopt, since any permanent addition 
to the equipment of the road should be charged to capital 
account and not to operating expenses. Assuming that 
we have the rate of capitahzation, if we divide the net 
income of the road by this rate of capitahzation it will 
then give a valuation of the property which represents 
its actual financial worth. The determination of the 
proper rate of capitalization is very difficult and must 
be determined according to some fixed rule rather than 
by assigning an arbitrary value. A minute difference 
in the rate of capitalization will produ*ce a very large 
difference in the resulting value of the road. The method 
adopted by the United States Department of Commerce 
and Labor may be very briefly indicated as follows: 



THE VALUATION OF RAILWAY PROPERTY. 49 

The market quotations on the securities of each railroad 
were studied for a period of over six months previous to 
a given date; even this period was extended in the case 
of abnormal fluctuations. The details of each issue of 
debt, the amount outstanding, the rate of interest, the 
dates of the payment of interest, and the date of maturity 
were determined. The effect of accrued interest and 
expected dividends on the prices of securities was allowed 
for. Since the record of sales only includes a very small 
proportion of the railroad securities in existence, even 
the bid and ask prices, which resulted in no sales, were 
considered. Under usual conditions the bid price repre- 
sents the lower limit of the market value of the security. 
The ask price represents the upper limit and the difference 
represents the zone within which bargaining takes place. 
On the general principle of adopting a lower valuation in 
case of doubt, the bid price was used as the basis upon which 
to value the securities considered. The actual return to 
a bondholder on a bond which matures at a given time is 
a very comphcated mathematical function of the annual 
interest rate and of the length of time still remaining 
for the bond to run. Sets of tables are published which 
give the average rate per cent in annual return on bonds 
purchased at various prices above or below par. The 
rate of annual return on bonds of the road, on the basis 
of their market price and the date of their maturity, was 
then figured for each issue of bonds. Multiplying this 
rate by the actual market value of the bonds gives the 
virtual annual return to the investor. Dividing the sum 
total of these annual returns by the sum total of the 
market values then gives the average rate of income on 
the bonds which were actually sold or on which bidding 
prices had been determined. The valuation of the funded 
debt, which was not quoted on the stock-market, was 
estimated by giving it a valuation corresponding with 



50 THE ECONOMICS OF RAILROAD CONSTRUCTION 

other similar securities. Multiplying these values by the 
same rate per cent per annum will give the annual return 
on the unhsted securities. We can then add up the values 
for the actual (or probable) market value of all the 
funded debt of the road and also the computed annual 
return to the investor and, by dividing the return by the 
total market value, we obtain the average annual return 
in rate per cent per annum. The market price of the 
stocks, together with their actual dividends, are similarly 
obtained, but there must be added to the market price 
of these stocks an estimate which will represent the 
undivided profits which have not been returned to the 
stockholders in the form of dividends. '^No well-managed 
corporation divides at any one time among its stockholders 
the precise amount of its gain since its last preceding 
dividend. Such a proceeding is not only impractical 
but also impossible, for the reason that it is impossible to 
tell precisely what the corporation gains have been during 
such a period. . . . The physical property has, to at 
least some extent, changed its identity during the period; 
the credits and obligations of the corporation have prob- 
ably changed; the general aspects of its business oppor- 
tunities have almost certainly changed; and all of these 
together have correspondingly modified the value of its 
physical property." Some of these improvements can be 
definitely allowed for. For example, the average annual 
expenditures for permanent improvements which have 
been made during a period of say five years should be 
added as though it were a dividend, since it might be 
considered as a dividend paid to the stockholder and 
immediately reinvested by him in the capital stock of 
the road. Similarly, variations in the profit-and-lcss 
account, as indicated by the general balance-sheet, can 
be allowed for by considering the average annual change 
in the profit-and-loss item for a period of years. Even if 



THE VALUATION OF RAILWAY PROPERTY. 51 

there had been a loss each year a steady reduction in 
that loss may be considered as an average increase in 
the profit account. 

Another item to be added is due to the fact that the 
sum of the actual annual payments of interest and guar- 
anteed dividends may amount to more than the computed 
annual return based on the market price of the bonds. 
This annual excess must be added in order to compute 
the actual annual return to the investors of the road. 
In fact the only object of computing the annual return, 
based on the market price and the time of maturity of 
the bonds, was that a proper average rate could be 
obtained on which to compute the return on the unquoted 
securities. There is still one other item which may need 
to be added: if the returns on the common stock are 
based on the present rate of dividends, but the dividends 
have varied during a period of say five years, which is 
the period adopted for the annual averages of betterment, 
etc., we must consider that a reduction in some rate of 
declared dividend means that so much money has been 
added to the profit-and-loss account of the road, and 
therefore the average amount of this difference, spread 
out during a period of say five years, represents the 
average addition (or deduction) which must be made 
to or from the average income of the road. Taking the 
summation of these average returns and dividing it by 
the summation of the market (and computed) prices of 
all forms of the securities of the road, we determine the 
actual average annual return in rate per cent on those 
securities. 

Dividing the net earnings of the road by this computed 
rate of capitalization then gives the valuation of the entire 
property. 



52 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

Legal Control. 

27. The subject of the legal control of railroad cor- 
porations by the federal, State, and municipal govern- 
ments is so very broad that several volumes would be 
required to adequately discuss even the present condi- 
tion of such regulation. A large part of the subject 
(the making of rates) is usually considered to be entirely 
outside of the province of the engineer, since the engineer 
is never called on to make rates or to revise them. But 
there are many cases where a knowledge of the method 
actually employed by railroad managers in making and 
revising rates, and the control which has already been 
exercised by the State and federal governments over rate- 
making, will give the engineer a much clearer idea of the 
influence which rate-making has on many of the problems 
which daily come before him. It may be more accurate 
to say that he should understand how little rate-making 
is affected by such variations in engineering design as he 
is able to control. In the next few pages an attempt will 
be made to very briefly state a few of the fundamental 
principles regarding the methods of rate-making and the 
control of rates which is exercised by the State and federal 
governments. 

28. Basis of freight-rates. — The usual method of setting 
a price on a manufactured conmiodity is to determine 
from actual experience what is the cost of manufac- 
turing the commodity and to add to such cost an amount 
which will pay a reasonable return on the capital invested, 
and also pay a reasonable return to the manufacturers 
to compensate them for their time, skill, and knowledge of 
the business. If the manufactured article is secured by 
patents and is in great demand, the profit added to the 
cost of the manufacturing will be correspondingly large, 
and yet even this is considered right since the owners 



THE VALUATION OF RAILWAY PROPERTY. 53 

of a valuable invention are entitled to a corresponding 
profit on the invention. Ever since legal control of 
railroad-rates has been suggested there has been an 
effort to establish a basis of cost of transportation, so 
that by adding a reasonable amount, which will pay for 
the use of the capital, a proper charge may be deter- 
mined, and that the railroad shall be enjoined from attempt- 
ing to collect any greater charge for such transportation. 
A consideration of some of the facts already stated, together 
with demonstrations made in subsequent chapters, will 
show that the cost of transportation is a very variable 
quantity. It will be shown that, even though we deter- 
mine from statistics of the whole country that the average 
cost of transporting one ton per mile is about .5c., we 
cannot therefore say that the cost of transporting one 
ton for one mile on any particular railroad and under all 
conditions will be .5 c. or even approximately so. Even 
if we were to establish from the statistics of any one 
given road that the average annual cost of transporting 
freight on that road amounted to a certain figure, it would 
be neither fair nor equitable to say that all traffic should 
be charged according to this figure, that no traffic should 
be taken at any less figure, nor that any charge could 
be made at any greater figure. To a very considerable 
extent it is true that railroad expenses are independent 
of the amount of business done. The fixed charges must 
be paid regardless of the amount of business, if the road 
is kept solvent. The cost of maintaining the road-bed and 
track is very largely independent of the amount of traffic. 
Whether there are twenty trains per day each way or 
only one, the amount of track-work which is necessary to 
keep the road up to a given standard will not be propor- 
tional to the number of trains. Although the fuel bill will 
vary more nearly in accordance with the amount of 
traffic, it will be by no means strictly in accordance with 



54 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

it. The practical result of all this is that railroad profits 
are subjected to ^'the law of increasing returns." The 
first half of the business which is done costs a large pro- 
portion of the total; the final ten per cent is almost clear 
profit. A railroad is very often compelled to accept 
some of its business at a rate which is much lower than 
the average rate or it cannot get the business at all. 
It can handle the additional business at a net additional 
cost which will be less than the amount received for it and 
hence can make a profit on such business. Under such 
conditions the business is profitable. If it is attempted 
to increase the charge for this low-grade business to the 
average rate for all business it will not get it at all. If 
it is attempted to reduce the charges on its local non- 
competitive business to the lower average rate actually 
received the road cannot pay its expenses and must go 
bankrupt. These facts may be illustrated by a very 
simple concrete example, in which the figures make no 
pretense of accuracy and are given merely for the purpose 
of illustrating a principle. Suppose that a road is hand- 
hng 80,000 tons of non-competitive freight per year; for 
which it receives $1 per ton; suppose that it has an 
opportunity of handling 80,000 additional tons of com- 
petitive freight at the rate of 60 cents per ton; its gross 
receipts are therefore $128,000. The competition is such 
that it must accept the competitive freight on the basis of 
60 cents or refuse it altogether. It is therefore handling 
160,000 tons of freight at an average rate of 80 cents per 
ton. Assume that it could handle its non-competitive 
business alone at a total expenditure, for operating ex- 
penses and fixed charges, of 90% of the amount received 
or $72^000 for the 80,000 tons. Assume that the extra 
business, whose cost is confined to comparatively small 
additions to the cost of maintenance of way, maintenance 
of rolling stock, and the expenses of conducting transpor- 



THE VALUATION OF RAILWAY PROPERTY. 55 

tation, costs but 50 cents per ton. The additional busi- 
ness is therefore handled at a cost of $40,000, and the 
entire traffic at a total expenditure of $112,000, which 
leaves a net profit of $16,000 on the business. Although 
the competitive business is handled at a far less rate 
than the non-competitive business the net profit on that 
part of the business alone is $8000, which is as great as the 
profit on the non-competitive business. If, in response 
to attempts to enforce uniform rates, the charges were 
cut down to the uniform basis of $128,000 on 160,000 
tons of freight or an average price of 80 cents per ton, we 
would find that the additional competitive freight could 
not be obtained at all. The road would then be compelled 
to attempt to pay its operating expenses by handling the 
80,000 tons of freight at 80 cents, which would give a rev- 
enue of only $64,000 when the actual expenses, including 
fixed charges, are supposed to cost $72,000. Such a 
condition of affairs could only lead to bankruptcy. The 
condition of competition is one that a road is forced to 
meet. 

29. Direct competition. — A road that is already bank- 
rupt is usually the one which most recklessly breaks 
established rates and starts a rate war. Such a road will 
enter the most reckless competition in order to obtain 
business under any conditions. A rate which will pay 
operating expenses, even though it necessitates a default 
of the interest on the bonds and, of course, pays no 
dividends, is doing better than to remain idle, since, if it 
pays the operating expenses, it is at least maintaining 
its road-bed and track in some sort of condition. There- 
fore such a road will try to obtain business at any rate 
which will actually pay the operating expenses. The solvent 
road which is so situated that it must meet the compe- 
tition of the road which is recklessly cutting rates has 
forced upon it the alternative of accepting business at 



56 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

much less than its usual rates or refusing it altogether. 
If the general manager can estimate that such business 
can be handled at a rate which will more than cover the 
additional operating expenses, he is justified in accepting 
the business, especially since it will actually prove a 
soiArce of profit to the road. It is claimed that these 
who ship their freight on the non-competitive high rates 
are helping to pay the freight of others. This is not 
true, since the others will not pay anything to the road 
except at the reduced rate. As a matter of fact, it might 
even be said that the low-rate shipper helps to pay the 
freight of the high-rate shipper, since the profits of 
the road are increased by the payments made by the 
low-rate competitive shipper, thus enabling the road to 
reduce the rates of the high-rate non-competitive shipper. 
We are thus led to the conclusion that freight-rates are 
not, and cannot be, based on any rational estimate of the 
cost of service. The railroads really charge ^^what traffic 
will bear," and this charge is determined very largely by 
causes over which the railroads have little or no control. 
This will be discussed later. 

30. Indirect competition. — It has frequently been stated 
in this book that the prosperity of a railroad company is 
very intimately connected with that of the conamunity 
which it serves. A large part of the business of a rail- 
road is freight business. The freight business of a rail- 
road depends on the business prosperity of its customers. 
Commercial competition requires that a manufacturer 
shall not only manufacture his goods as cheaply as his 
competitors, but that he shall also be able to deliver 
the goods at the very door of his customers as cheaply 
as another manufacturer. Since a very considerable item 
in this total cost is the cost of transportation, it becomes 
a matter of business for the railroad to assist the manu- 
facturer by making the freight-rate, if possible, at such a 



THE VALUATION OF RAILWAY PROPERTY. 57 

figure that it will permit the manufacturer to meet the 
competition of others. If the manufacturer cannot clo 
this, he cannot clo business at all, and the railroad com- 
pany loses his business altogether. This course of reason- 
ing is the justification of the cUscriminations which have 
been practiced by railroad companies in favor of certain 
shippers. These shippers could not do business profitably, 
except at certain freight-rates which were below the normal. 
The railroads could handle such business as extra business 
at a profit, and could make more money on such an arrange- 
ment than by not handling the business at all. Of course 
there are reasons which make such discriminations unjust 
as well as illegal, especially when these methods have 
been used to build up the wealth of great monopolies. 
A treatise of this sort is not the place to discuss discrimi- 
nations, but the above statements have been made to 
show why discriminations may be profitable to the rail- 
road company. The indirect competition furnished by 
other railroads, who are trying to build up their own 
prosperity by building up the prosperity of the shippers 
along their Hues, is one of the most potent causes to 
reduce freight-rates, even to a shipper who has absolutely 
no choice except to ship his goods on the one road which 
passes his place of business. The railroad company is 
therefore virtually compelled to reduce its freight-rates to 
a point where they will pay the operating expenses and 
leave as much margin as possible on the capital invest- 
ment. It will thus be seen that a profit which is made 
out of the low-grade competitive business will actually 
enable the railroad management to reduce the freight- 
rate on the so-called non-competitive business, if it is 
found necessary to do so in order that the local shipper 
may meet the competition of another shipper on a rail- 
road, perhaps 200 miles away. 



58 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

31. Justification of special commodity rates. — In the 
following chapter the methods of estimating the volume 
of traffic of a new railroad enterprise will be discussed. 
The discussion there chiefly concerns the methods of 
estimating the volume of the business. Although the 
freight-rates obtainable on such business wdll usually 
bear some relation to the similar rates charged by other 
railroads, the rates will not necessarily be identical. In 
fact the estimator must have sufficient knowledge of 
commercial business to know the market prices of com- 
modities in the markets reached by his road, and to know, 
for example, the market price of hay in a certain city 
and the rate that may be charged for transporting hay 
which will leave to the farmer a sufficient amount per ton 
to encourage him to raise and haul hay to the railroad 
for shipment. If the freight-rate charge is excessive, 
so that there is but little object for the farmer to raise 
hay, the railroad will lose such business altogether. It 
would be preferable for it to charge a lower rate per ton 
than is charged for other merchandise, rather than to 
discourage and lose the business altogether. 

32. Low rates on low-grade freight. — The preceding 
paragraph furnishes the basis of the justification of an 
apparent discrimination between different kinds of freight. 
From the operating standpoint it costs just as much to 
haul a ton of coal as to haul a ton of furniture or expensive 
machinery, and yet the universal custom is to handle coal, 
broken stone, and similar products which have compara- 
tively little value per ton, at a much cheaper rate than 
articles of higher value. This is partly done on the 
general principle that the traffic will bear a higher value. 
In the case of coal, even the low freight-rate is a large 
proportion of the total value of the coal. In the case of 
machinery or dry-goods, the freight charge is compara- 
tively ins.'gnificant. The shipment of low-grade, bulky 



THE VALUATION OF RAILWAY PROPERTY. 59 

freights would be considerably discouraged by a marked 
increase in the freight -rates. The much higher rates 
which are charged on high-grade freight is such a small 
proportion of their total value that their use is not appre- 
ciably limited by the freight-charges. 

'As a conclusion of this very brief discussion on freight- 
rates, it may be said that the fundamental principle of 
freight-rates is that the charge is made in accordance with 
what traffic will bear — interpreting this phrase to mean 
that the prosperity of the railroad is bound up with the 
prosperity of the community served, and that the railroad 
will have more business and obtain a greater profit by 
encouraging the business and permitting the prosperity 
of the community. And it will best accomplish this by 
reducing its freight-rates to the point which will so en- 
courage business that the return to the railroad company 
will be a maximum. 

Federal Control. 

33. Origin. — The authority for the control of railroads 
by the federal government is based not only on the principle 
of the governmental control of ^^ common carriers," but 
also on the provision of the Constitution that Congress 
has the power to regulate the commerce between States. 
It is quite probable that this provision was inserted 
in the Constitution chiefly, if not entirely, with the idea of 
preventing the collection of import and export duties on 
merchandise passing between the States. Railroads were 
non-existent at that time, were hardly even dreamed of, 
and certainly the framers of the Constitution had not the 
slightest conception of the present railroad situation. 
Nevertheless on this very slender basis has been built 
up the elaborate series of decisions which have been 
rendered by the U.S. Supreme Court in the many recent 



60 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

railroad cases. Of course it required no authority greater 
than that of common law for Congress to deal with railroads 
as common carriers which are subject to its jurisdiction. 
Inasmuch as the consohdation of railroads during recent 
years has made every important railroad system enter 
two or more States, there is but little railroad traffic in 
the country which is not subject to federal control. Federal 
control has been exercised partly as a result of the very 
extensive grants of public land which have been donated 
to railroad companies to encourage the building of im- 
portant roads, such as the Union Pacific Railroad. The 
authority of Congress to control railroads even to the 
making of reasonable freight-rates has been thoroughly 
affirmed by decisions of the U. S. Supreme Court. 
The control exercised by Congress over railroads has 
been principally centered on the regulation of freight- 
rates. In addition to this, acts have been passed to 
regulate the use of safety appliances, such as automatic 
couplers, air-brakes, etc. 

34. Necessity for control. — A private shipper has but 
little hope of satisfaction if he considers that a given 
freight-rate on a shipment of goods is unreasonable. If 
the goods have already been shipped, the charge must be 
paid before the goods can be recovered at the other end. 
Theoretically the law provides that he can complain to 
the Interstate Commerce Commission that the charge is 
uru*easonable. Although the Interstate Commerce Com- 
mission is empowered to order a railroad to reduce its 
charge to '^reasonable rates," it does not have the power 
to state what a reasonable rate shall be. Regardless 
of the Interstate Commerce Law, the shipper can bring 
an action against a railroad company in an ordinary 
court upon the complaint that a rate is unreasonable, 
and if he can estabhsh the point, the railroad must refund 
whatever has been proven to be the excess. But when the 



THE VALUATION OF RAILWAY PROPERTY. 61 

cost of such proceedings is taken into consideration, there 
is no object for the shipper to bring such an action either 
before the courts or the Interstate Commerce Commission. 
Even the powers of the Interstate Commerce Commission 
have been so hmited by the decisions of the Supreme 
Court that the shipper has very httle recourse under the 
present conditions of the law. The railroad company 
is protected by the constitutional provision that rates 
cannot be reduced to such an extent as to make them 
''confiscatory." But since it would be practically 
impossible to demonstrate that any individual rate 
would be confiscatory, the provision is of httle prac- 
tical use to the railroads. The reasonableness of a rate 
is very difficult to prove, except by a comparison with 
similar rates under similar conditions. The chief provi- 
sion of the Interstate Conamerce Act is what is commonly 
called the '^long-and-short-haul clause/' which forbids a 
railroad from charging more for a short haul than for a 
long haul in the same direction and under similar condi- 
tions, the short haul being included within the long haul. 
The words ''under similar conditions" have been the 
loophole which has practically nuUified the long-and- 
short-haul clause. The railroads have successfully main- 
tained the existence of a difference in operating conditions 
which justifies them in accepting some shipments of com- 
petitive freight at less rates than other shipments of non- 
competitive freight on which the haul was actually some- 
what less. 

35. Pooling. — Unrestricted competition on competitive 
freight has proved very disastrous to railroad companies, 
especially when they have endeavored to prevent their 
business from slipping away from them b}^ reducing their 
rates in order to meet competition below the point where 
it even paid the actual additional cost of operation. To 
avoid such cutthroat competition many competing rail- 



62 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

roads formed what were called pools, under which they 
agreed to maintain rates and to insure to each of the 
competing roads their proportion of the freight business. 
The passenger pools were sometimes arranged in the 
same way. The proportions assigned to each road were 
determined by the actual business of that road during 
the previous year. The pools were of two kinds, money 
pools and traffic pools. On the basis of the money pools, 
each road was allowed an agreed share of the total receipts 
on the business done by all the roads, almost regardless 
of the work which it actually did. Some slight adjust- 
ment was made by allowing roads which had handled 
more than their rated share of business a small extra 
amount which would partially compensate them for the 
extra work which they actually did. But the compensa- 
tion was purposely made so small that it would be no 
object for the railroad to attempt to get more than its 
share of business. The traffic pools were managed so 
that the actual traffic of the roads would be kept at the 
prearranged ratios, this being accomphshed by diverting 
traffic to roads which showed a tendency to fail to get their 
clue share. Since shippers usually object to the diversion 
of their freight shipments, certain large shippers, who were 
called ^^eveners," consented to allow their shipments to 
be diverted to any route so as to even up the traffic to 
the different roads. Of course they were allowed con- 
cessions in the freight-rate on account of this arrangement. 
But as poohng was popularly supposed to be detrimental 
to competition, it was declared illegal by federal legisla- 
tion and has been discontinued. 

36. Traffic associations. — It has been attempted to 
maintain competitive freight-rates between railroads by 
means of traffic associations. The traffic associations 
which have been formed have adopted uniform systems 
of classification together with uniform systems of freight- 



THE VALUATION OF RAILWAY PROPERTY. 63 

rate charges which would prevent rate-cutting. The 
many attempts in this direction have been rendered in- 
effectual, because the railroads themselves would not 
abide by the schedules. One freight agent would suspect 
(justly or otherwise) that another freight agent was cut- 
ting rates and he would proceed to meet the cut. A rate 
war would soon be in progress, which would probably 
disrupt the association. Even traffic associations were 
declared illegal, on the ground that they were " in restraint 
of trade." Traffic associations are still in existence, but 
their powers have been legally curtailed. Any attempt 
in their by-laws to discipline any road for an infraction 
of their rules is declared illegal. All agreements regarding 
rates are merely ^^gentlemen's agreements" and this gives 
no guarantee of immunity from a rate war. 

37. Consolidation. — Poohng and traffic associations 
having been declared illegal, the only method left to 
prevent competing roads from ruining each other finan- 
cially by means of rate wars was to cut off all incentive 
for competition by consolidation. Even this has been 
somewhat prevented by legal provisions against the con- 
solidation of parallel or competing lines. But such pro- 
hibitions have not prevented the elimination of competi- 
tion by combinations of groups of capitalists who so 
control the roads on the principle of '' community of 
interests" that there is practically no such thing as an 
active competition which has an effect in cutting down 
rates. Consolidation has already progressed to such an 
extent that the great railroads of the country are now 
combined into a very few groups and are owned or con- 
trolled by a comparatively small number of men. Since 
the reduction in rates through active competition is now 
practically hopeless, the only means of preventing the 
railroad from being the sole judge of how much it shall 
demand from a helpless shipper appears to lie in the 



64 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

power of Congress to directly specify what a traffic-rate 
shall, be. This power appears to be only limited by the 
common-law rule that ^4tmust be reasonable," which, of 
course, includes the constitutional provision that ''it must 
not be confiscatory." 

State Control. 

38. Scope and limitations. — ^The scope of State control 
is somewhat the same as that of federal control, but it has 
different limitations. It must be subject to federal control 
and cannot apply to any traffic except that in the State. 
Like the federal control its authority is based chiefly on 
the principle of a governmental control of common carriers. 
The control actually exercised by the States applies 
chiefly to police regulations as to their physical condition. 
Railroad charters are usually granted by State legislatures. 
These have already been discussed in Chapter II. The 
control by the States of such matters as grade crossings, 
etc., has also been referred to. Comparatively few of 
the States have interfered with the rates which shall be 
charged by a railroad, except as it has been done in the 
charters of the railroad. Even the limitations imposed by 
the charters are frequently so much higher than the rates 
which the railroad company themselves see fit to charge, 
that it cannot be said to have any influence on rate- 
making. Space is too fimited to discuss the so-called 
'^granger legislation," which was the all-important political 
controversy in the Northwestern States several years ago. 
The prevalent opinion that freight-rates were extortionately 
high produced very drastic legislation, cutting down the 
charges which the railroads were permitted to make. 
The legislation went too far, and the result was financial 
embarrassment and even bankruptcy for many of the roads. 
Much of this legislation has since been repealed. Some 



THE VALUATIOK OF RAILWAY PROPERTY. 65 

of the State Railroad Commissions, notably that of Texas, 
have been active in recent years in regulating the charges 
made by the railroads. It remains to be seen whether 
this action will prove beneficial alike to the railroads and 
to the communities. 

Other elements of State control have already been 
discussed in Chapter II. 



CHAPTER V. 

ESTIMATION OF VOLUME OF TRAFFIC. 

39. Primary considerations. — The economic considera- 
tions underlying the building of railroads are now funda- 
mentally different from those existing fifty or sixty years 
ago. In 1840 the number of miles of railroad in the 
United States was 2818. In sixty-four years that mileage 
was multiplied by more than 75. At that time the number 
of miles of line per 10,000 square miles (100 miles square) 
of territory was only 9.5. Now it is 720. At that time 
nearly the whole country was virgin territory, and it was 
not a question of the ultimate success of a road, provided 
it was constructed with a decent regard for sound engineer- 
ing principles, but a mere question of time before the 
country would develop sufficiently to support the road. 

In a broad way we may now say that the railroads of 
the country are built. The great trunk lines have developed 
practically all of the available east and west routes, at least 
between the Atlantic and the Middle West, and all of the 
necessary lines from north to south. More tracks will 
doubtless be built, but they will be the expansion of one- 
and two-track lines into four, or even six-track roads, 
or the construction of short stretches of expensive recon- 
struction to obtain low-grade lines. If irrigation succeeds 
in transforming parts of the great West from deserts into 
fertile farms, there will probably be an enormous increase 
in railroad building in the West, but even this will be 

66 



ESTIMATION OF VOLUME OF TRAFFIC. 67 

under different circumstances and conditions from those 
under which our raihoads were built during the period 
from 1860 to 1890. If we examine a railroad map of the 
United States, it will not be easy to find a spot in the 
New England States (except Maine), in the Middle Atlan- 
tic States, or in the States around the Great Lakes, which 
is 20 miles from any railroad. If we consider that the 
whole country was gridironed with railroads running north 
and south and east and west at a distance apart of 30 
miles, only one point in each square would be as far as 
15 miles from any road. Such squares would have 60 
miles of road for 900 square miles of territory or 6.67 
miles per 100 square miles of territory. The average 
for the whole United States (7.20) is even now greater 
than this. Florida and Texas are the only States east of 
the 100th meridian in which the number is less than 6.67. 
The practical meaning of the above is that the railroad 
building of the future, at least in the eastern part of 
the United States, will probably be confined to the con- 
struction of comparatively short cross-country lines 
whose chief purpose is to give additional facilities to 
sections of territory which already have railroad lines 
within ten to twenty miles. This again means that a 
railroad will not usually be able to monopolize all traffic 
in the territory through which it passes and for as many 
miles back from the railroad as railroad influence may be 
considered to extend, but that it must directly compete 
with other roads for its traffic. Of course it will have a 
virtual monopoly on sources of traffic which are so near 
to its line that no other road could obtain such traffic 
except at a prohibitive sacrifice, but it will mean that 
for some distance out of large cities, which are entered 
by several railroads from approximately the same direc- 
tion, the traflnc will be largely competitive. It will fre- 
quently be found that a very large proportion of the 



68 THE ECONOMICS OF RAILROAD CONSTRUCTION. 



traffic of a railroad is competitive traffic and that the 
strictly non-competitive traffic, the local traffic which 
it picks up from its own immediate territory, is compara- 
tively unimportant. On this account we must largely 
modify the methods of estimation which would have 
been proper many years ago and also estimates based on 
the history of roads which have been long established, 
since in general those roads began under traffic considera- 
tions which are different from those of a new road of the 
present day. 

40. Methods of estimating volume of traffic. — We may 
first begin with the most rapid, easy, and approximate 
methods which have their value, because their rapidity 
and simplicity renders them easy to apply and they at 
least form a valuable check on other and more elaborate 
methods. In Table III are shown the gross "earnings 

Table III. — Gross and Per-capita Railroad Earnings — Whole 
United States. 



Year. 


Gross earnings 

from operation 

(millions). 


Population 
(thousands). 


Earnings per 
capita. 


1894 

1895 

1896 

1897 

1898 

1899 

1900.. 

1901 

1902 

1903 

1904 


$1,073 
1,075 
1,150 
1,122 
1,247 
1,314 
1,487 
1,589 
1,726 
1,901 
1,975 


67,800 
69,100 
70,400 
71,700 
73,000 
74,300 
75,600 
76,900 
78,200 
79,500 
80,800 


$15.83 
15.55 
16.33 
15.65 
17.08 
17.95 
19.67 
20.66 
22.07 
23.91 
24.44 



from operation" for the whole United States for each 
year, from 1894 to 1904 inclusive, and in the next column 
the actual or estimated population. Dividing one by 
the other we have the average earnings per capita for the 
whole United States. It is interesting to note from this 



ESTIMATION OF VOLUME OF TRAFFIC. 



69 



the comparatively low value of these receipts in 1894, 
which immediately followed the panic year of 1893, and 
how, by an almost uniform rise, the receipts have in- 
creased about 60%. These values, after all, are but 
average values, and are the average of the whole ten sec- 
tions into which the area of the United States is divided 
by the Interstate Commerce Commission. By reference 
to the map of the United States shown in Fig. 4, it will 
be seen that the whole territory of the United States is 
divided into groups. These groups are found to vary 
considerably in the character of their population, its den- 
sity, the number of miles of railroad per hundred square 
miles of territory, and in the amount contributed per 
capita. In Table IV are shown the gross earnings for 
the year 1900 as divided among the different groups. 

Table IV. — Statistics of Mileage and Gross Earnings in Differ- 
ent Sections of the United States (1900). 







Number of 












miles of line 


Number of 


Gross earn- 






Mileage. 


per hundred 
square miles 


miles of line 
per 10,000 


ings per 
mile 


ings per 
capita. 






of 


inhabitants. 


operated. 






territory. 








Group I. . . . 


7,622 


12.30 


13.63 


$12,392 


$17.31 


II 


21,481 


19.88 


12.91 


16,514 


21.55 


Ill 


23,403 


18.66 


24.38 


9,273 


23.14 


IV 


11,894 


8.53 


20.71 


5,250 


10.39 


V 


22,672 


7.57 


21.05 


5,323 


10.62 


VI 


43,448 


11.73 


34.31 


6,727 


23.74 


VII 


10,930 


2.64 


66.49 


5,233 


35.05 


VIII 


23,775 


6.51 


37.80 


5,363 


20.30 


IX 


12,233 


3.74 


30.78 


4,664 


13.97 


X 


15,889 


2.09 


51.13 


6,349 


30.49 


United States . . 


193,346 


6.51 


25.44 


$ 7,722 


$19.67 



The figures in the last column are not based on data 
which are so accurate that the figures may be considered 
to be precise, but the errors involved are certainly small 
and the figures are amply accurate for our purpose. The 



70 THE ECOx^JOMICS OF RAILROAD CONSTRUCTION. 

figures are seen to vary considerably from the average 
receipts per head of population for the whole United 
States. As a general statement it is true that the estimated 
earnings for a road to be constructed in the territory cf 
any one of these ten sections would be given more accurately 
by the average figure for that section than by the figure 
given for the whole United States. Such a figure has its 
value as a first trial and preliminary estimate of the 
probable traffic of a road. 

41. Estimate of earnings per mile of road. — It is some- 
times attempted to quickly estimate the probable earnings 
per mile of road by a comparison of the earnings per mile 
of existing roads w^hich are similarly situated. The gross 
earnings per train-mile for every railroad in the United 
States are given in the statistics of the Interstate Com- 
merce Commission. We will consider first the gross 
earnings per mile of road and per train-mile for the ten 
greatest railroad systems of the country and will also 
consider similar figures for ten small railroads which are 
chosen at random, except that their mileage is invariably 
less than 100 miles and also that they are all independent 
railroads, and therefore it need not be considered that 
their gross earnings are dependent upon their relationship 
to a larger trunk system. These figures are given in 
Table V. 

An inspection of these figures will show that the gross 
receipts per mile of road are exceedingly variable, even 
for roads in the same section of the country and of approxi- 
mately the same mileage. On the one hand, it will be seen 
that the earnings per mile of road of the five small roads 
in Group II are all very much smaller than the average 
per mile of road for that group. The earnings per mile of 
road evidently bear a close relation to the frequency of 
the train service, and this of course is exceedingly variable. 
There is hardly a possibiUty of uniformity until we deter- 



ESTIMATION OF VOLUME OF TRAFFIC. 



71 



Table V 



-Gross Earnings per Mile of Road and per Train-mile 
FOR Great and Small Roads (1904). 



No. 




Mileage. 


Gross annual 
receipts. 


Gross 
earn- 
ings 


Re- 
port. 


Per mile 
of road. 


Per mile 
of road for 
that group. 


per 
train- 
mile. 




Whole United States 


220,112 


$9,306 




$1 94 








5'^ 


Canadian Pacific 

C. B. & Q 


8,382 
8,326 
7,412 
7,197 
6,761 
5,619 
5,031 
4,489 
4,374 
4,229 


$5,540 
7,640 
7,190 
6,270 
5,580 
8,300 
8,330 
8,080 

10,710 
4,860 




SI 92 


1412 




2 04 


1407 


Chicago & Northwestern . 

Southern Railway 

C. R. 1. &P 

Northern Pacific 

A. T. & S. F 

Great Northern ... . 




1.71 


939 




1.49 


1433 




1.64 


1534 




2.66 


1383 




2.17 


1471 




2 94 


1242 


Illinois Central .... 




1 58 


975 


Atlantic Coast Line 

Averasre of ten 




1 67 












$ 7,250 




$1 98 










78 
134 
349 
374 
396 


Montpelier & Wells River. 

Somerset Railway Co 

Hunt. & Broadtop Mt . . . 
Lehigh & New England. . 
Ligonier Valley 


44 
42 
66 
96 
11 
59 
55 
51 
20 
50 


$ 4,095 
2,960 
11,560 
1,990 
6,570 
2,910 
3,625 
1,770 
4,510 
7,560 


13,994 
13,994 

1 

1 
20,187 

11,863 
6,679 
5,443 


$1 45 
1.35 

ri.82 

1 1.14 

i 2 06 


486 

660 

769 

1239 

1835 


Newburgh, Dutch. & Conn . 

Susquehanna & N. Y 

Detroit & Charlevoix . . . 
Harriman & Northeast'n 
Galv., Hous. & Henderson 

Average of ten, . 


1 1.08 

[1.74 

2.11 

2.73 

3.29 






$4,755 




$1 88 













mine the average revenue per train-mile, which is also 
given in Table V. In this case, however, there is a uni- 
formity which is really remarkable in spite of the varia-^ 
tions which are seen. It may be noted that the average 
revenue per train-mile for the large roads is much more 
nearly uniform and that it closely approximates to the 
average value for the whole United States as might have 
been expected. The revenue per mile from the smaller 
roads, while it covers a far larger range than in the case 
of the larger systems, is nevertheless a figuie with some 



72 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

limitations. It seldom drops below $1, and the cases 
are rare where it rises above $3. But even such a figure 
is of but little value until the proper number of train- 
miles per year may be determined^ and this after all 
brings us back to the point where we started, viz., the 
determination of the amount of traffic from which we 
may obtain an idea as to the number of trains. It is 
perfectly true, as elaborated later, that on roads of very 
small traffic the number of trains will not be strictly 
proportional to the number of passengers carried nor to 
the gross number of the tons of freight. Nevertheless, 
if the number of trains is increased in order to encourage 
traffic, the revenue per train-mile will be reduced, although 
it is sometimes a wise proceeding to do so. 

42. Estimate of tributary population. — Having decided 
on some estimate for the receipts per head of tributary 
population, even if it is only for a preliminary and rough 
estimate, the next step is to determine the number of 
the tributary population. A large map with a scale of 
say one mile to the inch is of considerable assistance 
in determining this. On this map, which may be one of 
the easily obtainable railroad maps or a set of maps 
such as are published by the U. S. Geological Survey, 
we may see the location of all existing railroads. The 
proposed road will probably pass to some extent through 
territory considered exclusively its own. If it passes 
through a valley, so that it is separated on either side 
by high hiUs from the valleys occupied by other railroad 
lines which are perhaps ten miles away, it may reasonably 
claim all of the population within the valley through 
which it passes. The population of this area may be 
determined with sufficient accuracy from census records 
or other sources. Where the road passes through towns 
which are already served by one or more lines, it is not 
right to consider that the entire population of that town 



ESTIMATION OP VOLUME OF TRAFFIC. 73 

will contribute per annum the average per-capita quota. 
In fact it would be more nearly true to say that the per- 
capita quota multiplied by the population of the town 
will be distributed among all the roads concerned in the 
relative proportion of their importance. Or, in other words, 
if we divide the population of the town into parts which 
are proportional to the relative importance of the roads, 
we may consider that the income from that town will 
equal that proportion of the total population multiplied 
by the average per-capita figure. By thus computing 
the tributary population for each section of the road 
we may multiply the sum total by the assumed per- 
capita figure and obtain a rough estimate of the gross 
receipts. 

43. Estimate by comparison with other roads. — Still 
another method of estimating the gross revenue from 
operation is to obtain the figures of the gross revenue of 
an existing road which is operating under conditions 
which are similar to those of the proposed line. This 
might be done by saying that since the existing line has 
gross receipts of so much per mile, and since the proposed 
line will have very similar advantages, the receipts per 
mile of road should be substantially the same. Perhaps 
a still better method than the above would be to estimate 
the tributary population of the existing road by the 
method indicated in the last section. An estimate should 
then be made of the population which would be tributary 
to the proposed line. Dividing the gross receipts of the 
existing line by its tributary population would give a 
fairly reliable estimate of per-capita receipts from such a 
community. Multiplying this figure by the tributary 
population of the proposed line would then give a fairly 
close estimate of its probable revenue. Probably the 
greatest danger underlying the above method comes 
from the inaccuracy of the assumption that the existing 



74 THE ECONOMICS OF RAILROAD C0x\^STRUCT10N. 

road and the proposed road will operate under similar 
conditions or that their tributary populations will have 
equal revenue-producing capacities. An experienced man 
may however use this method by making a suitable 
allowance when he considers that the proposed road will 
be more valuable or less valuable than the line with which 
it is compared. Even though this method is confessedly 
inaccurate and subject to error, it should generally be 
utilized, because it is nearly always possible to obtain 
sufficient data for the purpose with but Httle trouble, 
and the results obtained are a valuable check on the 
results which will be computed by the other methods. 

44. Actual estimation of the sources of revenue. — Prac- 
tically the only accurate method of making any such 
computations is to study the entire territory which will 
be served by the road and estimate in detail the amount 
of business which will be obtained from every manu- 
facturing plant, mine, lumber-camp, and even every farm. 
Through country cUstricts and through towns which are 
not already served by a railroad such an estimate is not 
very difficult. Generally the errors will be on the safe 
side, unless rendered valueless by a gross exaggeration of 
the expected increase in business. A factory which 
can do business without railroad facilities will frequently 
multiply its business many times when it is connected 
with the outside world by a railroad which passes its 
doors. It is usually safe to estimate a freight-charge 
not only on the entire present output of the factory, bnt 
to even consider that the factory will grow and furnish 
a much larger amount of business. An experienced 
estimator will soon estimate the probable yield of the 
farms which are within five miles of the road and what 
would be the probable market for the produce when 
it became possible to ship it by rail. In estimating what 
farms should be thus included the distance from the 



ESTIMATION OF VOLUME OF TRAFFIC. 75 

farm (perhaps in an opposite direction) to another rail- 
road and also the nature of the roads and the hills should 
be taken into consideration. It is usually possible to 
predict with certainty that a farmer who had previously 
hauled his entire output over a steep hill for a distance 
of seven or eight miles to an existing road will transfer 
his entire business to the new road because the new road 
will be only three miles away and the grade is downhill. 
It may even be justifiable to consider that the farmer 
will produce more of certain kinds of crops, since the 
accessibility to the markets produced by the proposed 
road will encourage him and will enable him to make 
profits which were unobtainable before. Of course the 
estimator must have sufficient knowledge of mercantile 
values to know what are the probable markets, not only 
for farm^-produce, lumber, and minerals, but also for 
manufactured products. The estimator will consider each 
proposed station on the road in turn and will estimate 
(considering first the freight business) that the farms 
within reach of that station will annually bring to that 
station so many tons or car-loads of various kinds of 
farm-produce which will probably be shipped to a certain 
market, or at least will be shipped from that station to one 
or the other of the termini of the road where they will 
connect with other lines. Multiplying that tonnage of 
produce by a suitable freight-rate for the distance will 
determine the receipts for those items. Each lumber 
tract, each mine and each factory should be considered 
in the same way. Unless there is some place along the 
line where certain products are consumed the traffic of 
this kind will usually run from the local station to one 
or the other of the termini. Of course there will be a 
small amount of local freight traffic between stations 
along the line, but this is usually a comparatively small 
proportion of the business done. 



76 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

45. Estimation of passenger traffic. — Statistics show 
that the proportion of the passenger revenue to the total 
earnings is roughly constant, and yet it varies considerably 
in the different groups. This is best shown in Table VI. 



Ta 


bleVI 


.— Pu 


BLic Service of Railwa-^s 


, BY Groups (1900). 






. 


cd 


Passenger service. 


Freight service. 








"0. 
t 








pas- 
arried 
per 

ine. 




0% 


tons 
t car- 
mile 

of 


u 


3 






C 02" 
bC 


a 


o^iS^ 


« Sc 


_o 1 


■^-SSrS 


c'^ 




d 




II 


a 




III 








It 






IS 


'a 

C3 


il§s 


^'S.2 


ft 


t-^'^t^ 


1 = 2 


P 







PM 


W 


12; 


< 


< 


^ 


< 


< 




Pass. 


38.05 


$6.59 














Ij 


Frt. 


53.47 


9.26 


259,503 


60 


18.46 


572,796 


178 


82.76 


Other 


8.48 
















n^ 


Pass. 


22.04 


4.75 














Frt. 


71.59 


15.43 


202,902 


47 


20.74 


1,900,578 


355 


110.91 




Other 


6.37 
















r 


Pass. 


20.22 


4.68 














in| 


Frt. 


72.22 


16.74 


94,154 


39 


35.18 


1,221,286 


329 


117.S2 


Other 


7.56 
















f 


Pass. 


20.99 


2.18 














IV^ 


Frt. 


71.72 


7.46 


46,543 


32 


38.59 


620,143 


296 


203.80 


I 


Other 


7.29 
















V 


Pass. 


19.98 


2.12 














Frt. 


71.94 


7.65 


45,263 


28 


38.63 


467,703 


203 


116.06 


I 


Other 


8.08 
















f 


Pass. 


19.53 


4.64 














VI j 


Frt. 


71.73 


17.04 


62,115 


35 


32.48 


586,524 


244 


143.64 


I 


Other 


8.74 
















f 


Pass. 


18.82 


6.60 














VII 1- 


Frt. 


73.47 


25.77 


41,323 


39 


91.48 


360,370 


217 


204.73 


l 


Other 


8.21 
















f 


Pass. 


18.59 


3.77 














VIII ^ 


Frt. 


72.66 


14.76 


42,794 


31 


46.36 


385,193 


186 


170.75 


I 


Other 


8.75 
















f 


Pass. 


18.29 


2.55 














IX ^ 


Frt. 


74.69 


10.44 


37,266 


32 


52.97 


363,278 


198 


173.21 


I 


Other 


7.02 
















f 


Pass. 


25.90 


7.90 














x^ 


Frt. 


67.14 


20.49 


77,873 


60 


37.45 


394,355 


261 


237.07 


I 


Other 


6.96 


















Pass. 


21.77 


4.28 












Whole 

U.S. 


Frt. 


70.56 


13.88 


83,295 


41 


27.80 


735,366 


271 


128.53 


Other 


7.67 

















ESTIMATION OF VOLUME OF TRAFFIC. 77 

By examining this table in connection with the map of the 
United States (Fig. 4) showing the different groups, much 
may be learned regarding the character of these groups, 
and the effect of that character on railroad earnings. 
For example, in Group I (the New England States), al- 
though the gross earnings per capita are smaller than the 
average, the passenger earnings per capita are large, and this 
is in spite of the fact that the average journey per passen- 
ger (18.46 miles) is less than in any other group. Freight 
earnings, however, have a lower percentage in this group 
than in any other. The average haul per ton and the 
number of tons in a train is less than any other group. On 
the other hand, Group VII (see Table VI), which includes 
the States of Montana, Wyoming, Nebraska, and portions 
of Colorado and the Dakotas, pays a larger amount per 
capita to the railroads than any group in the United 
States. This is largely due to its enormous freight 
business, which furnishes nearly three-fourths of the 
total earnings with a gross amount equal to $25.77 per 
capita. Even the passenger earnings are $6.60 per capita, 
which is more than 50% of excess of the average for the 
United States. The average journey per passenger was 
91.48 miles, which is far in excess of that in any other 
group and between three and four times the average for 
the whole United States. The railroads in Groups IV 
and V have the lowest earnings per capita. The per- 
centages of passenger and freight business are in each 
case about equal to the average for the country, but 
the earnings per capita are very small. Another rare 
and abnormal case is found in Group X, the Pacific Coast 
States. This section of the country has ^'magnificent 
distances." The average haul of each ton of freight is 
237 miles, which is nearly twice the average, and the 
average freight and passenger earnings per capita are 
in each case about 50% in excess of the average. Such 



78 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

differences in the characteristics of the various sections 
of the country must be kept in mind when making any 
estimate of the expected traffic on a proposed Hne. 

CoMditions which Affect Volume of Traffic. 

46. Proximity to sources of traffic. — It has elsewhere 
been emphasized that the most important general require- 
ment of the locating engineer is that he shall so locate the 
road that it shall obtain the maximum business. Every 
other requirement should be subordinate to this. This 
is unquestionably the best policy, since in the long run 
the road which best serves the community will obtain 
the greatest business. 

The construction of a railroad through a large city, or 
even into the heart of a large city which may be a terminus 
of the road, is a very expensive matter. The engineer and 
the board of directors are confronted with the almost 
irresistible temptation to avoid at least a part of such 
expense by placing the station (or the terminus) farther 
and farther from the heart of the city. Generally the 
loss of business resulting from such supposed economy 
is not directly apparent to the non-expert, especially if 
there is no competition, and even the expert will have 
difficulty in accurately estimating the loss. But we may 
learn from past experience, and there are fortunately 
several conspicuous examples of the relative volume of 
business obtained by competing roads whose traffic 
facilities are very different. In the early '80's, the entire 
line of the New York Central and the Lake Shore & 
Michigan Southern between New York and Chicago was 
practically paralleled by a competing line. The older 
roads were built during the early history of railroad 
building, went through the heart of every city and village, 
and into the very centers of their termini. At the time 
the competing roads were constructed, access to the 



ESTIMATION OF VOLUME OF TRAFFIC. 79 

business centers of these cities and villages was far more 
difficult and expensive. At Painesville, Ohio, for example, 
the Lake Shore road passes within a block or two of the 
chief business streets. The depot of the ^'New York, 
Chicago, and St. Louis R.R." was about three-fourths of 
a mile out of town and could be reached only by an 
unpaved country road. In other places the relative traffic 
facilities were about as unequal. In New York City the 
N. Y. Central penetrates the city to its terminus at 42d 
St. The West Shore terminal at Weehawken is not only 
much farther in an air-line distance from the business 
center of the city, but is separated by a river only to be 
crossed by a ferry, and even then the traveler is landed 
on the river-front and a long tedious street-car ride is an 
essential for nearly all. Under such circumstances, the 
cutthroat competition which ensued between the two 
roads could only have one possible ending. Excluding 
from consideration the strictly local non-competitive 
traffic, the '^West Shore" and the ''^Nickel Plate" could 
not hope to obtain any of the through competitive pas- 
senger business except by a ruinous cut in rates. Of course 
the older roads were much better able financially to 
endure the rate war and, although it affected their divi- 
dends, the effect on the new roads was bankruptcy, receiver- 
ships, and sales under foreclosure. The unequal struggle 
for freight business was about as hopeless for the new 
roads. In New York City, where such a large proportion 
of the freight-terminal transfers are made by shifting 
freight-cars on floats, the West Shore had a fighting 
chance, but in the smaller cities and villages, the merchant 
or manufacturer frequently had the choice of hauling 
freight a block or two over paved streets to the old railroad, 
or hauling it half a mile or a mile over an unpaved country 
road to the new railroad. Of course the new road was 
compelled to make some concession, either by reduced 



80 THE ECONOMICS. OF RAILROAD CONSTRUCTION. 

freight-rates or by free teaming, to equalize the difference. 
The net result was the same — financial ruin. Possibly 
it may be said that the promoters of the West Shore and 
Nickel Plate never expected their roads to compete on 
equal terms — that the projects were really blackmailing 
schemes to compel the older roads to buy them out. Even 
if this is so, the history of the competition of these roads 
is an instructive example of the effect of unequal facilities 
on the traffic obtainable from a community. 

Another very instructive example of the effect of a 
difference in facilities affecting the traffic is given in the 
competition of the P. K.R. and the B. & 0. R.R. for 
passenger business between Philadelphia and Baltimore. 
The P. R.R., by an expenditure aggregating millions, has 
made its Philadelphia terminal under the very shadow 
of the City Hall. The B. & 0. R.R., although it paid out 
very large sums for its entrance into the city, made its 
terminal at Twenty-fourth and Chestnut streets. What- 
ever may be the reason that the terminal was not placed 
nearer the City Hall, the fact remains that it is over a 
mile away, and a street-car ride is almost an essential for 
the great bulk of its passenger traffic. The terminal as con- 
structed, although not comparable with Broad St. Station 
(P. R.R.), is far larger than the business of the road requires. 
The waiting-room has been fittingly described as ^ lone- 
some." The student should note that a handicap on 
facilities not only affects business but literally kills certain 
classes of business. In spite of the enormous expendi- 
ture made by the B. & 0. R.R., its facifities do not equal 
those of the P. R.R., and the result is ruinous for com- 
petitive passenger business. 

47. Estimation of effect of location of station at a dis- 
tance from the business center. — So many factors enter 
into such a question that no exact solution is possible. 
The chief factor is the proportion of competitive business. 



ESTIMATION OF VOLUME OF TRAFFIC. 81 

On business where there is direct competition the road 
with less facihties must either give up the competition 
for such business or offer some compensating advantage 
which will probably consume nearly all, if not quite all, 
of the profits on such business. On other business 
which is non-competitive the disadvantage will not be 
so great, although even here it must not be ignored. 
The late A. M. AVellington attempted to answer this 
question by the statement that the location of a station 
one mile from the heart of the town will affect the business 
from that town anywhere from 10 to 40%, depending on 
the circumstances, and that 25% might be considered an 
average figure. For each, succeeding mile he deducted 
25% of the remainder. Of course such an estimate is at 
its best a very loose approximation. 

48. Extent of monopoly in railroad business. — A very 
common mistake among railroad promoters is to assume 
that a railroad passing through any section of country 
will be able to collect ^'all the traffic there is," disregarding 
for the present any competition from another road. This 
idea is probably responsible for many of the blunders 
w^hich have caused a road to be located in a way that 
hampered traffic, when the only object gained was a very 
insignificant economy in the first cost of the road. The 
student should not forget that railroad traffic varies in 
its character from the absolutely necessary traffic, for 
which any reasonable or even unreasonable sum would 
be paid, to the extreme of unnecessary traffic, such as 
traveling for pleasure, which is absolutely dependent 
upon the facilities offered. Even freight business depends 
on the total cost of transporting goods from their location 
in a factory or mine to the very door or warehouse of 
the consumer. The laws of competition require that the 
manufacturer must be able to manufacture his goods and 
deUver them to the door of the consumer in a distant city 



82 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

as cheaply as his rival can deliver goods of the samci 
quality at the same destination. Anything which facili- 
tates such transportation, not only affects the factory or 
mine, but it may make all the difference between profit 
and loss on the whole transaction. Therefore the pros- 
perity, not only of the railroad, but also of the mining and 
manufacturing interests, depends on the promotion of 
railroad facilities. In a town where there is no competition 
the railroad may have a monopoly so far as any other 
railroad is concerned, but, unless facilities are created to 
handle goods with economy and to transport passengers 
conveniently, the amount of traffic developed will be 
very greatly reduced. The strictly necessary traffic which 
a railroad might claim as a monopoly is so very small 
that very few railroads could pay their operating expenses 
from it. The dividends of a road are declared out of 
the last small percentage of the revenue, and such revenue 
comes from the unnecessary traffic, which must be coaxed 
and encouraged, and which is so very easily affected by 
the lack of faciUties and conveniences. 

Perhiips the best general statement which may be 
made regarding the question of locating a station near 
the business center of the town is that it depends on the 
limit of capital which may properly be put into the enter- 
prise, provided the project as a whole is not financially 
wrecked by the expenditure. There is hardly a limit of 
expenditure which would not prove a paying investment 
in course of time in order to locate a road within a block 
of the business center of a town. It should never be con- 
sidered as a project which may be deferred, since the 
price of land invariably increases and usually multiplies 
many times after the road has been constructed, so that 
a future construction into the he^rt of a town or city 
becomes almost prohibitive unless at enormous expense. 



PART II. 

OPERATING ELEMENTS OF THE PROBLEM. 



CHAPTER VI. 

OPERATING EXPENSES. 

49. Classification of operating expenses. — The following 
classification of operating expenses follows the system 
adopted by the United States Interstate Commerce Com- 
mission for many years, not only because the method of 
division is probably as good as could be devised for the 
purpose, but also because it will render the following dis- 
cussion uniform with their system and therefore permit 
the utilization of the values given by them. The expenses 
are first divided into four groups, which are as far as pos- 
sible independent of each other. The average value for a 
period of ten years (from June 30, 1894, to June 30, 1904) 
is as given in the table on page 84. 

It should be remembered that the figures are ex- 
clusively percentages. The growth of railroad business 
has been so uniform that the gross amount spent for each 
item, and even subitem, is usually larger with each suc- 
ceeding year, even though the percentage of that item 
to the gross expense is smaller. 

50. Average operating expenses per train-mile. — The 
reports published by the Interstate Commerce Commission 
give the operating expenses per train-mile for nearly all 

83 



84 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

Average value, 

1. Maintenance of way and structures 21 .034% 

This value ranges between a minimum of 19.519% 
in 1904 to 22.272% in 1901. 

2. Maintenance of equipment 18 . 024% 

The percentage of this item has varied from 15.761 
in 1895 to 19.967 in 1904. With two shght excep- 
tions this item has regularly increased each year, 
not only in gross amount, but also in the percent- 
age of this expense to the total. 

3. Conducting transportation 56. 636% 

The percentage of this item has varied from 59.460 
in 1895 to 54.671 in 1902. Although the gross 
amount has largely increased, the ^percentage of 
this item has been decreasing with almost uniform 
regularity. 

4. General expenses 4 .306% 

The percentages of this item are nearly uniform, 
varying from 3.789% in 1903 to 4.756% in 1897. 



100.000% 

of the railroads of the country. In fact the omissions are 
almost exclusively those of the very insignificant railroads 
on which the bookkeeping and tabulating of expenses is 
not kept up with sufficient accuracy to furnish such figures. 
The very surprising feature of these figures is that the 
operating expenses per train-mile are so nearly uniform. 
Although there are numerous instances where the average 
cost of running a train per mile over any one road has a 
large variation from the average figure for the whole 
United States, it will be found that the cases of very large 
variation are comparatively rare, and it will also be found 
that when the variation is very large there is usually 
some abnormal operating condition which accounts for the 
unusual value. The average cost of running a train one 
mile for the whole United States, as given for each year, 
is given in Table VII. The variation is shown graphically 
in Fig. 6. 

The enforced economies following the panic of 1893 
brought down expenses to the low point given for 1895. 



OPERATING EXPENSES. 



85 



Table VII. — Avefl\ge Cost per Til\in-mile for Whole United 
States— 1890-1904. 



Year. 


Average cost per train- 
mile, cents. 


Year. 


Average cost per train- 
mile, cents. 


1890 


96.006 


1898 


95.635 


1891 


95.707 


1899 


98.390 


1892 


96.580 


1900 


107.288 


1893 


97.272 


1901 


112.292 


1894 


93 . 478 


1902 


117.960 


1895 


91.829 


1903 


126.604 


1896 


93.838 


1904 


131.375 


1897 


92.918 







From this point the rise has been almost steady, until the 
annual cost is nearly 50% higher than in 1895. This has 































-■ 


120 
110 
100 










.' 














/ 


y 






; 




2 










^^ 


[^ 


/ 








1 


i 

a 








/ 


y 








^ 












.^ 


^^ 












90 
80 
70 
60 
50 
40 
30 




a 


2 






































































































































































































10 






























































130 
120 
110 
100 

90 



5 6 7 § 9 1900 1 2 

Fig. 6.— Average cost per train-mile in cents. 

been partly due to an increase in wages and salaries, and 
partly due to the increased cost of fuel and suppUes; but 



86 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

in spite of this increase, the uniformity between roads of 
various amounts of traffic is still remarkable. In Table 
VIII are given values showing the operating expenses per 
train-mile for ten of the largest railroad systems in the 
country, and also for ten small roads whose mileage is 
less than 100 miles. 



Table VIII. — Operating Expenses per Train-mile on Large and 
Small Roads (1904). 



No. in 
Report. 



52 
1412 
1407 

939 
1433 
1534 
1383 
1471 
1242 

975 



78 
134 
349 
374 
396 
486 
660 
769 
1238 
1835 



Whole United States. 



Canadian Pacific 

C. B. &Q 

Chicago & Northwestern. 

Southern Railway 

C. R. I. &P. 

Northern Pacific 

A. T. &S. F 

Great Northern 

Illinois Central 

Atlantic Coast Line. . . . 



Average of ten. 



Montpelier & Wells River 

Somerset Railway Co 

Huntingdon & Broadtop Mountain. 

Lehigh & New England 

Ligonier Valley 

Newburgh, Dutchess & Connecticut 

Susquehanna & New York 

Detroit & Charlevoix. , 

Harriman & Northeastern. . , 

Galveston, Houston & Henderson. . 



Average of ten. 



Mileage. 



220,112 



8,382 
8,326 
7,412 
7,197 
6,761 
5,619 
5,031 
4,489 
4,374 
4,229 



44 
42 
66 
96 
11 
59 
55 
51 
20 
50 



Operat- 
ing ex- 
penses 
per train- 
mile. 



1.314 



1.320 
1.313 
1.136 
1.048 
1.199 
1.392 
1.305 
1.464 
1.107 
0.984 



1.227 



1.169 
0.802 
0.950 
0.793 
1.427 
0.922 
1.368 
1.424 
2.162 
1.556 



1.257 



Ratio, 
expenses 
to 
earn- 
ings. 



67.79 



68.72 
64.35 
66.61 
70.30 
72.90 
52.26 
60.05 
49.72 
70.02 
58.95 



63.39 



80.73 
59.37 
52.10 
69.80 
69.33 
85.09 
78.47 
67.52 
79.26 
47.27 



68.89 



In Table VIII the ten large railroad systems represent 
the ten largest railroads of the country. The ten small 
roads were chosen almost at random, except that the 
operating mileage is invariably less than 100 miles and 



OPERATING EXPENSES. 87 

the roads are all classified as ''independent roads," so that 
their operating expenses need not be considered as being 
unduly affected in one way or the other by their relations 
to any corporation controlling them. It may be noted 
that, although the average cost per train-mile is more 
uniform in the case of the larger railroad systems, as 
might have been expected, and that the variations from 
the average are much greater in the case of the small 
roads, the variations doubtless being due to special and 
local conditions, nevertheless the small roads show operat- 
ing expenses per train-mile which are sometimes above 
and sometimes below the average values for the whole 
country or for the larger systems, but their average does 
not greatly differ from that of the average of the large 
systems. Without attempting to elaborate the explana- 
tion of the causes of this uniformity, it may be seen in 
general that although the larger railroads have very large 
expenses, which on the smaller roads are very small (if 
they exist at all), yet, since the divisor (the number of 
trains) on the large road is so very large, the quotient, 
which is the average cost per mile, tends to become uni- 
form. It should also be noted that the ratio of earnings 
to expenses on the ten large systems and on the ten small 
roads remains at a fairly constant figure. 

51. Itemized classification of operating expenses. — The 
reports made to the U. S. Interstate Commerce Com- 
mission are given according to such a standardized 
system that the entire operating expenses of the railroads 
of the country (with the exception of about one-sixth of 
one per cent) may be classified. Although such detailed 
figures are not published for each railroad, the averages 
for all the railroads are published each year. The com- 
parison of the percentages for each year are very instruc- 
tive, especially when it is possible to trace the cause of 
the fluctuations in those percentages. The classification 



8S THE ECONOMICS OF RAILROAD CONSTRUCTION. 

Table IX. — Summary showing Classification of Operating Ex- 

OF Each Class to Total for the 



Item. 

Maintenance of Way 
and Structures. 
Repairs of roadway. . . . 

Renewals of rails 

Renewals of ties 

Repairs and renewals of 

bridges and culverts. . 
Repairs and renewals of 

fences, road crossings, 

signs, and cattle-guards. 
Repairs and renewals ol 

buildings and fixtures. . 
Repairs and renewals of 

docks and wharves .... 
Repairs and renewals ol 

telegraph 

Stationery and printing. . . 
Other expenses 

Total 

Maintenance of Equip- 
ment. 

Superintendence 

Repairs and renewals of 

locomotives 

Repairs and renewals of 

passenger- cars 

Repairs and renewals ol 

freight- cars 

Repairs and renewals of 

work-cars 

Repairs and renewals of 

marine equipment 

Repairs and renewals of 

shop machinery and 

tools 

Stationery and printing. . . 
Other expenses 

Total 

Conducting Transporta- 
tion. 

Superintendence 

Engine- and roundhouse- 
men 

Fuel for locomotives 

Water-supply for locomo- 
t\v(^s, 



Amount, 1904. 




Per cent. 




1904 


1903 


1902 


$138,300,607 
17,345,483 
33,668,58£ 


10 . Mi 
1.29S 
2.51C 


11.093 

1.386 

2.487 


11.331 
1.521 

2.838 


29,778,004 


2.228 


2.461 


2.593 


5,839,385 


.437 


.527 


.625 


28,697,616 


2.147 


2-590 


2.562 


2,789,094 


.206 


.235 


.220 


2,385,300 

392,801 

1,669,816 


.179 
.029 
.125 


.165 
.032 
.209 


.173 
.031 
.361 


S260,866,691 


19.519 


21.185 


22.255 


$ 7,572,965 


.567 


.559 


.601 


105,633,752 


7.904 


7.408 


7.246 


26,078,106 


1.951 


2.044 


2.157 


103,932,132 


7.777 


7.442 


7.432 


3,081,998 


.231 


.242 


.245 


2,065,442 


.154 


.177 


.215 


9,411,076 

566,948 

8,515,198 


.704 
.042 
.637 


.696 
.046 
.519 


.643 
.044 
.544 


$266,857,617 


19.967 


19.133 


19.127 


$ 23,533,951 


1.761 


1.742 


1.711 


125,440,824 

158,948,886 


9.386 
11.893 


9.562 
11.675 


9.401 
10.776 


8,894,551 


.666 


.614 


623 



OPERATING EXPENSES. 



89 



PENSES FOR THE YeAR ENDING JuNE 30, 1904, AND PROPORTION 

Years ending June 30, 1904, to 1895. 









Per cent. 








Average 

ten 
years. 




1901 


1900 


1899 


1898 


1897 


1896 


1895 


6 


10.924 
1.676 
3.14C 


10.995 
1.138 
3.036 


10.720 
1.322 
2.901 


10.643 
1.391 
3.232 


10.644 
1.546 
3.357 


10.738 
1.444 
3.028 


10.235 
1.499 
2.948 


10 . 767 
1.422 
2.948 


1 
2 
3 


2.730 


2.703 


2.374 


2.512 


2.472 


2.265 


2.268 


2.461 


4 


.598 


.616 


.487 


.537 


.509 


.561 


.520 


.542 


5 


2.417 


2.466 


2.181 


1.957 


1.745 


1.794 


1.648 


2.151 


6 


.283 


.308 


.254 


.245 


.231 


.270 


.2.35 


.24c 


7 


.158 
.02C 
.317 


.153 
.030 
.352 


.142 
.026 
.446 


.137 

.025 
.349 


.126 
.024 
.318 


.135 
.027 

.372 


.134 
.033 
.304 


.150 
.029 
.315 


8 

9 

10 


22.272 


21.797 


20.853 


21.028 


20.972 


20.634 


19.824 


21.034 




.59c 


.597 


.632 


.656 


.667 


.666 


.629 


.617 


11 


6.695 


6.730 


6.208 


5.887 


5.663 


5.978 


5.660 


6.538 


12 


2.277 


2.263 


2.164 


2.188 


2.265 


2.216 


2.211 


2.174 


13 


7.436 


7.687 


7.038 


7.210 


6.376 


7.193 


6.008 


7.16C 


14 


.23S 


.252 


.210 


.159 


.140 


.145 


.121 


.198 


15 


.234 


.251 


.247 


.242 


.215 


.173 


.167 


.207 


16 


.043 
.507 


.604 
.043 
.502 


.512 
.040 
.544 


.486 
.038 
.493 


.478 
.039 
.509 


.520 
.040 
.460 


.455 
.041 
.469 


.57C 
.04S 
.518 


17 
18 
19 


18.62C 


18.929 


17.595 


17.359 


16.352 


17.391 


15.761 


18.024 




1.726 


1.831 


1.767 


1.744 


1.845 


1.731 


1.718 


1.757 


20 


9.340 
10.602 


9.476 
9.80£ 


9.690 
9.478 


9.64c 
9.457 


9.922 
9.392 


9.733 
9.669 


9.917 
10.408 


9.607 
10.316 


21 
22 


.612 


.590 


.6K 


.64f 


.677 


.691 


.7241 


.647 


23 



90 THE ECONOMICS OF RAILROAD CONSTRUCTION. 



Table IX (continued). — Summary showing Classification of 
Proportion of Each Class to Total for 



24 

25 

26 
27 

28 

29 
30 
31 
32 

33 

34 

35 

36 
37 
38 

39 
40 
41 
42 
43 

44 

45 
46 



Item. 



Oil, tallow, and waste for 
locomotives 

Other supplies for locomo 
tives 

Train service 

Train supplies and ex- 
penses 

Switchmen, flagmen, and 
watchmen 

Telegraph expenses. . . . 

Station service 

Station supplies 

Switching charges — bal- 
ance. 

Car per diem and mileage 
— balance 

Hire of equipment — bal 
ance 

Loss and damage 

injuries to persons 

Clearing wrecks 

Operating marine equip 
ment 

Advertising 

Outside agencies 

Commissions 

Stock-yards and elevators 

Rents for tracks, yards, 
and terminals 

Rents of buildings and 
other property 

Stationery and printing. . . 

Other expenses 



Total. 



General Expenses. 

Salaries of general officers. 

Salaries of clerks and at- 
tendants 

General office expenses 
and supplies 

Insurance 

Law expenses 

Stationery and printing 
(general offices) 

Other expenses 



Total. 



Grand total. . 



Amount, 1904. 



$ 5,460,629 

3,351,739 

88,237,172 

20,777,084 

57,909,962 
23,362,675 
86,339,58£ 
10,361,992 

3,985,153 

20,340,343 

5,738,952 
17,002,602 
15,838,17c 

3,631,352 

11,074,030 

5,937,816 

19,563,159 

822,212 
2,738,499 

19,694,025 

5,103,561 
8,557,541 
4,726,400 



Per cent. 



1904 



$757,372,878 



$ 11,234,945 

17,552,570 

3,080,718 
6,289,915 
6,856,870 

2,272,390 
4,091,731 



$ 51,379,139 



$1,336,476,325 



.409 

.251 
6.602 

1.555 

4.333 

1.748 
6.460 

.775 



1.522 

.429 

1.272 

1.185 

.272 

.829 
.444 
1.464 
.062 
.205 

1.474 

.382 
.640 
.353 



1903 



56.670 



.841 

1.313 

.230 
.471 
.513 

.170 
.306 



3.844 



100.000 



.389 

.232 
6.677 

1.552 

4.313 

1.754 

6.664 

.667 

.244 

1 . 400 

.214 
1.094 
1.120 

.284 

.745 
.428 
1.449 
.044 
.057 

1.544 

.411 
.642 
.376 



55 . 893 



.823 

1.254 

.234 
.432 
.541 

.175 
.330 



1902 



.366 

.218 
6.737 

1.500 

3.984 

1.784 

6.832 

.676 

.272 

1.480 

.180 

.990 

1.048 

.221 

.721 
.429 
1.579 
.077 
.069 

1.519 

.440 
.622 
.416 



3.789 



100.000 



54.671 

.925 

1.244 

.249 
.412 
.558 

.168 
.391 



3.947 



100.000 



OPERATING EXPENSES. 



91 



Operating Expenses for the 


Year ending June 30, 


1904, and 


THE Years ending June 30, 1904, to 1895. 






Per cent. 


Average 

ten 
years. 




1901 


1900 


1899 


1898 


1897 


1896 


1895 


i 


.361 


.365 


.359 


.355 


.374 


.379 


.413 


.377 


24 


.206 
7.011 
1.471 


.188 
7.244 
1.467 


.177 

7.583 
1.527 


.156 
7.660 
1.525 


.160 
7.589 
1.508 


.229 
7.784 
1.556 


.200 
7.993 
1.526 


.202 
7.288 
1.519 


25 
26 

27 


3.848 

1.785 

6.947 

.672 


3.944 

1.812 

7.103 

.679 


4.149 

1.906 

7.510 

.696 


4.080 
1.907 

7.758 
.692 


4.171 

2.000 

8.002 

.751 


4.120 

1.978 

7.710 

.794 


4.160 

2.078 

8.112 

.876 


4.110 

1.875 
7.310 

.728 


28 
29 
30 
31 


.319 


.340 


.356 


.331 


.327 


.356 


.344 


.319 


32 


1.618 


1.800 


2.010 


2.107 


2.203 


2.054 


2.096 


1.829 


33 


.161 
.819 
.911 
.189 


.223 
.764 
.910 
.173 


.368 
.734 
.874 
.147 


.342 
.706 
.884 
.130 


.249 
.692 
.874 
.123 


.322 

.775 
.840 
.126 


.384 
.784 
.945 
.130 


.287 
.863 
.959 
.179 


34 
35 
36 
37 


.862 
.428 
1.615 
.089 
.075 


.866 
.432 
1.519 
.151 
.060 


.868 
.438 
1.781 
.194 
.115 


.958 
.417 
1.762 
.181 
.155 


.934 
.428 
1.727 
.158 
.140 


.826 

.417 

1.567 

.16S 
.126 


.848 
.429 
1.623 
.154 
.116 


.846 
.429 
1.609 
.128 
.112 


38 
39 
40 
41 

42 


1.724 


1.728 


1.901 


1.914 


1.953 


1.746 


1.727 


1.723 


43 


.440 
.638 
.510 


.464 
.653 
.579 


.487 
.627 
.670 


.475 
.583 
.624 


.501 
.633 

.587 


.502 
.616 
.547 


.497 
.589 
.669 


.460 
.624 
.533 


44 
45 
46 


54.979 


55.179 


57.031 


57.194 


57 . 920 


57.362 


59.460 


56.636 




.984 


1.041 


1.171 


1.165 


1.235 


1.213 


1.333 


1.073 


47 


1.262 


1.269 


1.334 


1.334 


1.368 


1.409 


1.385 


1.317 


48 


.257 
.384 
.625 


.262 
.349 
.571 


.292 

.372 
.710 


.285 
.395 
.655 


.301 
.436 
.791 


.311 

.446 
.725 


.315 

.487 
.806 


.274 
.418 
.650 


49 
50 
51 


.161 
.447 


.166 
.437 


.171 
.471 


.176 
.409 


.163 
.462 


.165 
.344 


.172 
.457 


.169 
.405 


52 
53 


4.120 


4.095 


4 . 521 


4.419 


4.756 


4.613 


4.955 


4.306 




100.000 


100.000 


100.000 


100.000 


100.000 


100.000 


100.000 


100.000 





92 THii: ECONOMICS OF RAILROAD CONSTRUCTION. 

itself is shown in Table IX. The variations in the prin- 
'cipal items, especially those in which the engineer is inter- 
ested, will be briefly discussed. Many of the items are 
directly affected by differences in operating management, 
and many of them are affected by such changes in aline- 
ment as an engineer may be able to make. Such items 
call for particular study on the part of the engineer. On 
the other hand, many of the smaller items are almost in 
the nature of fixed charges which will not be materially 
affected by any change which may be made by the locating 
engineer or by any slight change of policy in the operation 
of the road. Such items will only be materially affected 
by some radical difference in the scale of operation of the 
road. 

Maintenance of Way and Structures. 

52. Item I. Repairs of roadway. — This item constitutes 
nearly one-half of the total cost of maintenance of 
way and structures. It might almost be said to include 
the maintenance of everything except such items as are 
specifically mentioned in the succeeding items. It 
includes practically everything which is usually spoken 
of as track-work, and also the maintenance of embank- 
ments, snow-fences, dikes, and retaining-walls. It in- 
cludes the cost of maintaining frogs, switches, switch- 
stands and interlocking-signals. The larger part of this 
item is that due to labor, which is chiefly track-labor. 
The percentage of this item increased from 1895 to 1902 — 
^ince then it has declined somewhat. It should likewise 
be noted that the average wages paid to trackmen have 
been increasing since 1894. The low point was reached 
in 1897-8 at $1.16 per day and in 1904 it was SI .33. 
The wages of section foremen have varied in about the 
same way. The average of this item for the past ten 
years has been 10.767%, while the total variation from 



OPERATING EXPENSES. 93 

this figure has been about .5% either way, the low figure 
occurring with one exception (in 1898) when the cost of 
track-labor was a minimum. 

53. Item 2. Renewals of rails. — This item, being one 
of the largest of the single items in the total cost of track 
maintenance, is considered separately. Its cost is very 
readily determined, since it consists of figures which are 
easily obtainable. It includes the cost of the rails, their 
inspection and their delivery to some specified delivery 
point on the track. The distribution of the rails each to 
the place where it is to be used is considered as part of the 
track-work and its cost is included in Item 1. The item 
is far more variable than Item 1. Its average value for 
the past ten years has been 1.422%, but during that 
time it has varied from 1.138% to 1.676%. These 
extremes occurred in succeeding years. Of course such 
fluctuations are due chiefly to a fluctuation in the price 
of rails but also to a variation in the standard of main- 
tenance. The item includes all rails wherever used, whether 
on main track, siding, repair track, gravel track, or on 
w^harves or coal-docks. It even includes guard-rails, but 
does not include any rail attachments, such as joints, frogs, 
switches, etc. 

54. Item 3. Renewal of ties. — This item averages over 
twice the cost of the renewal of rails, but the fluctuations 
are not quite as large a percentage of the item itself. 
The significance of the item corresponds closely with 
that of rails. It includes the cost of the ties, but not 
the cost of distributing them or placing them in the 
track. It does, however, include the cost of tie-plates 
and tie-plugs and also any chemical treatment which 
may be used. It would be expected that with the increas- 
ing scarcity of timber the cost of tie-renewals would be 
greater year by year, but there does not seem to be any 
indication of a uniform increase in cost. In fact the 



94 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

highest percentage during the last ten years occurred in 
1898. 

55. Item 4. Repairs and renewals of bridges and culverts. 
— This item includes the maintenance, cost of all bridges, 
trestles, viaducts, and culverts. It also includes all piers, 
abutments, riprapping, etc., necessary to maintaining 
them and the cost of operating drav^bridges. The average 
cost of the item for ten years has been 2.461%, and the 
variations have been quite small with no noticeable 
tendency to grow uniformly greater or less. The locating 
engineer is but little concerned with this item, since it 
usually does not figure except in specific instances, which 
must be specifically considered in his calculations about 
a proposed change of line. So far as the maintenance 
of small bridges and culverts are concerned it would 
usually be sufficiently accurate to consider that a pro- 
posed change of line, involving perhaps several miles of 
road, would require substantially the same number of 
bridges and culverts, and therefore that the cost of main- 
taining them would be the same by either line. The error 
involved in such an assumption would usually be insigni- 
ficant, unless there was a very large and material difference 
in the two lines in this respect. Under such conditions 
special computations should be made. 

56. Items 5 to 10. Repairs and renewals of fences, road- 
crossings, and cattle-guards — of buildings and fixtures — of 
docks and wharves — of telegraph-plant; stationery and 
printing, and " other expenses."^ — These six items have 
a sum total of a little over 3%. Their fluctuations are 
small and are usually due to causes which are beyond the 
control of the engineer and which will be unaffected by 
any reasonable change of plans which the engineer may 
make. In Item 5 are included not only those things 
which are specifically mentioned but also those structures 
which in general are not directly affected by the running 



OPERATING EXPENSES. 95 

of trains. For example, road crossings include not only 
the maintenance of highway crossings at grade but also 
overhead highway crossings and whatever a railroad 
may have to pay for the maintenance of a bridge by 
which another railroad crosses it. On the other hand, 
the maintenance of a bridge by which a railroad crosses 
another road (highway or railroad) is charged to bridges. 
Item 6 includes the cost of maintaining all buildings which 
are used to facilitate transportation, such as roundhouses 
and coaling-stations, water stations, sand-houses, sig- 
naling-towers, and passenger and freight stations. It 
also includes such miscellaneous structures as turntables 
and track-scales. Fixtures include cranes, derricks, office 
furniture, etc. Item 6 is a large one with considerable 
fluctuation, but railroad location has little or no influence 
on it. A possible exception is noted at the end cf 
§ 86. Items 7 to 10 are exceedingly small and the 
engineer has still less chance of influencing them in any 
way. 

Maintenance of Equipment. 

57. Item II. Superintendence. — The item averages 
about two-thirds of one per cent and has so little fluctua- 
tion under ordinary conditions that it may almost be con- 
sidered as a fixed charge. It includes those fixed charges 
in superintendence which do not fluctuate with small 
variations in business done. It includes the salaries of 
superintendent of motive power, master mechanic, master 
car-builder, foreman, etc., but does not include that of 
road foreman of engines nor enginemen. Although the 
item will vary with the general scale of business on the 
road, it does not fluctuate with it and hence will not 
usually be influenced by any small changes in alinement 
which the engineer may be considering. 



96 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

58. Item 12. Repairs and renewals of locomotives. — 
This subject will be treated at greater length in Chapter 
VII, Motive Power. The item is of interest to the locating 
engineer because he must appreciate the effect on loco- 
motive repairs and renewals of an addition to distance. 
This will be further considered in Chapter XII. A 
large part of the repairs of locomotives are due to the 
wear of wheels, which is largely caused by curvature. 
Therefore the value of any reduction of curvature is a 
matter of importance, and this will be considered in 
Chapter XIII. A considerable portion of the deteriora- 
tion of a locomotive is due to grade, and the economic 
.advantages of reductions of grade will be considered in 
Chapters XIV to XVII. 

This item includes the expenses of work whose effect 
is supposed to last for an indefinite period. It does noi 
include the expense of cleaning out boilers, packing cylin- 
ders, etc., which occurs regularly and which is charged 
to Item 21, roundhouse-men. It does include all current 
repairs, general overhauling, and even the replacement 
of old and worn-out locomotives by new ones to the 
extent of keeping up the original standard and number 
Of course additions beyond this should be considered as 
so much increase in the original capital investment. 
As a locomotive becomes older the annual repair charge, 
becomes a larger percentage on the first cost, and it 
may become as much as one-fourth and even one-third of 
the first cost. When a locomotive is in this condition it 
is usually consigned to the scrap-pile, the annual cost 
for maintenance becomes too large an item for its annual 
mileage. The effect on expenses of increasing the weight 
of engines is too complicated a problem to be solved 
accurately, but certain elements of it may be readily 
computed. While the cost of repairs is greater for the 
heavier engines^ the increase is only about one-half as 



OPERATING EXPENSES. 97 

fast as the increase in weight — some of the subitems not 
being increased at all. This will be further discussed in 
Chapter VII. 

59. Items 13, 14, and 15. Repairs and renewals of pas- 
senger-cars — of freight-cars — and of work-cars. — Many of 
the economic features of car construction, especially the 
effect of modern improvements, such as friction draft-gear, 
automatic couplers, and air-brakes, will be considered in 
Chapter VIII. Such figures will be utilized in considering 
the effect on car repairs of additional distance, of variations 
in curvature, and of grade as discussed in Part III. During 
the past five years there has been a gradual reduction in 
the percentage of this item for passenger-cars, but such a 
period is too short to determine whether this reduction 
is merely a chance fluctuation or an indication of a policy 
which will continue. On the other hand, the repairs and 
renewals of freight-cars have increased rather than dimin- 
ished. The fluctuations of this item are largely due to 
accidents rather than to any line of policy under the 
control of the engineer. It should be understood that 
for these items, as well as the previous item, the renewal 
of rolling stock generally means the construction of 
higher-grade locomotives and higher-grade cars. When 
this is done the difference in cost between the higher-grade, 
and probably more expensive, construction and the former 
cheap construction should be considered as an addition 
to the capital account rather than a charge against oper- 
ating expenses. The enormous increase in the movement 
of freight during the last few years has required a corre- 
sponding increase in freight-car equipment. Some roads 
have been charging up the full cost of the renewing of 
their old-fashioned light-weight equipment with more ex- 
pensive equipment under the head of operating ex- 
penses, and it is quite possible that a portion of the 
increase in I ten; 14 is due to this pohcy. 



98 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

60. Items 16, 17, 18, and 19. Repairs and renewals of 
marine equipment — of shop machinery and tools; station- 
ery and printing; other expenses.— The location of the 
road along the line has no connection with the maintenance 
of marine equipment. The maintenance of shop machinery 
and tools can only be affected as the work of repairs of 
rolling stock fluctuates, and of course in a much smaller 
ratio. No change which an engineer can effect will have 
any appreciable influence on this item. 

The other items are too small and have too little con- 
nection with location to be here discussed, except as it 
may be considered that they vary with train-mileage, 
which an engineer may influence (see Chapter XXIII, 
Grades). 

Conducting Transportation. 

61. Item 20. Superintendence. — This item averages 
about 1.75% and is only subject to small fluctuations. 
It will not be appreciably varied by any change of policy 
which the engineer may adopt. 

62. Item 21. Engine- and roundhouse-men. — This item 
includes the wages of engineers, firemen, and all men 
employed around engine-houses except those making 
such repairs as should be charged to the maintenance of 
equipment. A distinction is made between the two classes 
of roundhouse work on engines, one of which is considered 
the regular routine work, such as cleaning boilers, etc., 
and the other comprising those larger operations which 
may be considered as "maintenance of equipment." 
The roundhouse-men are usually paid by the day, but 
their total wages amount to about 9% of the total of Item 
21. On the other hand, enginemen are necessarily paid 
by the trip, except on the very small railroads. On very 
short roads, where a train crew can make two, three, or 



OPERATING EXPENSES. 



99 



even four complete round trips per day, they may readily 
be paid by the day, so many round trips being considered 
as a day's work, but on roads of great length, where all 
trains, and especially freight-trains, are run day and night, 
week-day and Sunday, all trainmen are necessarily paid 
by the trip or, as it is more usually expressed, by the 
^^run.'' It is generally found convenient to divide the 
road into "divisions" which are approximately 100 
miles in length. According as the division is greater or 
less than 100 miles, it is designated as a 1| run, li run, or 
perhaps | run. The enginemen will then be paid accord- 
ing to the number of runs made per month. There is a 
considerable fluctuation in the average wages paid in 
different sections of the United States, as is shown by the 
tabular form given below, in which the '^groups" refer 
to the sections into which the country has been divided 
by the Interstate Commerce Commission, as is shown 
in Fig. 4. This tabular form may be of some assistance in 
showing the average daily compensation which must be 
allowed for in the various sections of the country. 

Average Daily Compensation by Groups — 1904. 



Enginemen 
Firemen. . . , 



$3.55 
2.02 



II. 



$4.06 
2.33 



III. 



$3.99 
2.33 



IV. 



$4.19 
1.95 



$4.25 
2.09 



VI. 



$3.98 
2.39 



VII. 



$4.17 
2.47 



VIII, 



IX. 



$4.28 $4.32 
2.62| 2.56 



X. U.S. 



$4.97 
2.97 



$4.10 
2.35 



The actual wages paid to enginemen have been growing 
almost steadily between 1894 and 1904, the increase in 
that time being about 14%. Firemen are paid about 55% 
to 60% as much as enginemen, but their wages have 
likewise been steadily increasing from 1894 to 1904. In 
spite of this very large increase in wages and therefore 
absolute increase in the total amount paid, the 'percentage of 
Item 21 has in general declined between 1894 and 1904, 
as is shown by Table IX in the first part of the chapter. 



LOFa 



100 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

This shows that in spite of the very considerable increase 
in wages the cost of running a railroad has increased in 
a still faster ratio. The fluctuations of this item are of 
importance to the locating engineer in discussing the 
economics of differences in distance. This feature will 
be more fully discussed in Chapter XII. 

63. Item 22. Fuel for locomotives. — This item includes 
every subitem of the entire cost of the fuel until it is 
placed in the engine-tender. The cost therefore includes 
not only the first cost at the point of delivery to the road, 
but also the expense of hauling it over the road from the 
point of delivery to the various coaling-stations and the 
cost of operating the coal-pockets from which it is loaded 
on to the tenders. Even though the cost may be fairly 
regular for any one road, the cost for different roads is 
exceedingly variable. There has been a steady increase in 
the percentage of the cost of this item per train-mile from 
1897 to 1904. The item amounted to nearly 12% of the 
total operating expenses in 1904, and required an actual 
expenditure of nearly $159,000,000. It is the largest item 
in the whole cost of railroad operation. Although some 
roads, w^hich traverse coal-regions and perhaps actually 
own the coal-mines, are able to obtain their coal for a cost 
which may be charged up as $1 per ton or less, there are 
many roads which are far removed from coal-fields which 
have to pay $3 to $4 per ton, on account of the excessive 
distance over which the coal must be hauled. Unfortu- 
nately the figures pubhshed by the Interstate Commerce 
Commission do not show the variations in the percentage 
of this item in the different groups. In the various chap- 
ters of Part III will be shown the effect on fuel consump- 
tion of the several variations in location details. The 
great importance of this item requires that it shall be 
thoroughly understood and studied by the engineer. It 
will be shown, contrary to the commonly received opinion. 



OPERATING EXPENSES. 101 

that the fuel consumption is quite largely independent of 
distance and even of the number of cars hauled. 

64. Items 23, 24, and 25. Water-supply; oil, tallow, 
and waste; other supplies for locomotives. — Although 
the percentage cost of the water-supply has fluctuated con- 
siderably during ten years, there is but little indication of 
any permanent increase or decrease in the percentage. 
It is quite largely a fixed charge, since it is frequently 
furnished by municipalities at flat rates. There is but 
little reason to anticipate any increase in the cost, except 
as the general increase in the scale of expenditures might 
cause an increase in the absolute cost per train-mile. Of 
course this would not affect the percentage, although, since 
the cost per train-mile has been steadily increasing, a con- 
stant percentage will indicate a constantly increasing cost 
per train-mile. The other items of locomotive supplies are 
very small and are usually found to fluctuate very closely 
with the variations in the cost of water. Since the con- 
sumption of all these supplies will vary nearly as the 
engine mileage, the engineer is concerned with them 
directly to the extent to which he may change to the 
engine mileage. 

65. Item 26. Train service. — This item is one of the 
largest single items and includes in general the wages of all 
the train-hands except the engineman and fireman. As 
in the case of the engineman the train-hands are usually 
paid according to the number of runs. The item is there- 
fore of importance to the locating engineer from the one 
standpoint of distance, and even then only when the 
variation of distance, which is considered, will affect the 
classification of the run and therefore the rate of pay for 
that run. As in the case of the engineman and fireman 
there has been an almost uniform increase in the average 
daily compensation paid to these trainmen from 1894 to 
1904. The statistics of the Interstate Commerce Commis- 



102 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

sion give not only the average wages paid to conductors 
and other trainmen for the whole United States, but also 
the average for each group. As might have been expected 
the figures fluctuate considerably with the different groups, 
but it will be found that the fluctuations vary quite regu- 
larly with the fluctuations in receipts and operating ex- 
penses per train-mile in the different sections. This means 
that the general scale of wages and of living expenses in 
different parts of the country vary approximately in the 
same ratio. 

66. Item 27. Train supplies and expenses. — These 
items, which average about 1.5%, include the large Hst 
of consumable supplies, such as lubricating-oil, illuminat- 
ing-oil or gas, ice, fuel for heating, cleaning materials, etc., 
which are used on the cars and not on the locomotives. 
The consumption of some of these articles is chiefly a 
matter of time. In other cases it is a function of mileage. 
The effect of changes which an engineer may make on this 
item will be considered when estimating the effect of the 
changes. 

67. Items 28, 29, 30, and 31. Switchmen; flagmen and 
watchmen; telegraph expenses; station service; and 
station supplies. — The expenses chargeable under these 
items are very obvious from the titles. Many subitems, 
which are very small or which are of occasional or acci- 
dental occurrence, are also included under these items for 
lack of a better classification. The largest single item of 
these four is that of station service, which has averaged 
7% for the last ten years. Although it may have no 
special significance, the percentage of this item has been 
declining for seven or eight years past. In general the 
items are proportional to the general scale of business of 
the road, and are very largely independent of small fluc- 
tuations in business or of any changes which an engineer 
may be able to make. 



OPERATING EXPENSES. 103 

68. Item 32. Switching charges. — Wliere two or more 
railroads intersect there will be a considerable amount of 
shifting of cars, chiefly freight-cars, from one road to the 
other. This shifting at any one junction may be done 
entirely by the engines of one road or perhaps by those 
of both roads. A portion of the expense of this work is 
charged up against the other road by the road which does 
the work. The total amount of this work is carefully 
accounted for by a clearing-house arrangement, and the 
balance is charged up against the road which has done the 
least work. The item is very small, is fairly uniform 
year by year, and is seldom, if ever, affected by changes of 
alinement. 

69. Item 33. Car per diem and mileage — balance. — 
This item is a charge paid by one road to another for the 
use of cars, which are chiefly freight-cars. To save the 
rehandling of freight at junctions, the policy of running 
freight-cars from one road to another is very extensively 
adopted. Since the foreign road receives its mileage pro- 
portion of the freight charge, it justly pays to the road 
owning the car a rate which is supposed to represent the 
value of the use of the freight-car for the number of miles 
traveled. The foreign road then loads up the freight-car 
with freight consigned to some point on the home road and 
sends it back, paying mileage for the distance traveled on 
the foreign road, a proportional freight charge having been 
received for that service. All of these movements of 
freight-cars are reported to a car association, which, by a 
clearing-house arrangement, settles the debit and credit 
accounts of the various roads with each other. Such is the 
simple theory. In practice the cars are not sent back to 
the home road at once, but wander off according to the 
local demand. As long as a strict account is kept of the 
movements of every car, and as long as the home road is 
paid the charge which really covers the value of lost ser- 



104 THE ECONOMICS OF HAILROAD CONSTRUCTION. 

vice, no harm is done to the home road, except that some- 
times, when business has suddenly increased, the home 
road cannot get enough cars to handle its own business. 
The value of the car is then abnormally above its ordinary 
value, and the home road suffers for lack of the rolling 
stock which belongs to it. Formerly such charges were 
paid strictly according to the mileage. This developed the 
intolerable condition that loaded cars would be run onto a 
siding and left there for several days, simply because it 
was not convenient to the consignee to unload the car 
immediately. On the mileage basis the car would be earn- 
ing nothing, and, since the road on which the car then was 
had no particular interest in the car, the car was allowed 
to stand to suit the convenience of the consignee. To 
correct this evil a system of per-diem charges has been 
developed, so that a railroad has to pay a per-diem charge 
for every foreign car on its lines. To reduce this charge 
as much as possible the railroads compel consignees, under 
penalty of heavy demurrage charges, to unload cars 
promptly. The running of freight-cars on foreign lines 
is now settled almost exclusively on the per-diem basis, 
but the earning of passenger-cars over other lines, as is 
done on account of the advantages of through-car service, 
as well as the running of Pullmans and other special cars, 
is still paid for on the mileage basis. To the extent to 
which this charge is settled on the mileage basis, any 
change in distance which the engineer may be able to 
effect in the length of the road will have its influence on 
this item, but when the freight-car business, which com- 
prises by far the larger part of the running of cars over 
foreign lines, is settled on the per-diem basis no changes 
in alinement which the engineer may make will have any 
influence on the item. The item averages about 1.8%. 
For the past five years it has been considerably less than 
for the previous five years, which apparently indicates that 



OPERATING EXPENSES. 105 

the strict enforcement of the regulations regarding per- 
diem charges have made the railroads far more careful in 
the conduct of such business, and hence has reduced the 
charge. 

70. Items 35, 36, and 37. Loss and damage ; injuries to 
persons; clearing wrecks. — These expenses are fortuitous 
and bear no absolute relation either to the number of miles 
of road or the number of train-miles. While they depend 
largely on the standards of discipline on the road, even the 
best of roads have to pay some small proportion of their 
earnings to these items. While we might expect that a 
road with heavy traffic would have a larger proportion of 
train accidents than a road of light traffic, it is usually true 
that on the heavy traffic roads the precautions taken arc 
such that they are usually freer from accidents than the 
light traffic roads. During recent years there has been a 
very perceptible increase in the percentages of these items, 
particularly in the compensations paid for '' injuries to 
persons." The increase in this item coincides with the 
increase already noted in the number of passengers killed 
during recent years. The possible relation between curva- 
ture and accidents has already been discussed, but other- 
wise the locating engineer has no concern with these items. 

71. Items 38 to 53.— All of the remaining items, as 
stated in Table IX, are of no concern to the locating engi- 
neer. They are either general expenses, such as the 
salaries of general officers, insurance or law expenses, or 
are special items, such as advertising or the operation of 
marine equipment which will not be changed by any 
variations in distance, curvature, or grades which a locating 
engineer may make. There is therefore no need for their 
further discussion here. 

72. Estimation of the effect on operating expenses of a 
change in alinement,— It has already been shown that 
the cost of a train-mile is marvelously uniform on roads 



106 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

of varying character. The cost of running a train one 
mile has therefore been taken as the unit of value on 
which to base calculations as to the effect of changes in 
ahnement. The general method is to take up each item 
in turn of the cost of operating trains, and to estimate 
the effect of a change in alinement on each item of 
expense. Some of the items are changed very materially. 
Others are practically unaffected. By careful study of 
the situation, it is usually possible to estimate with reason- 
able accuracy that each proposed change in alinement 
would affect each item by a certain percentage of the 
average value of that item. If we then multiply the normal 
percentage of each item by the total percentage by which 
the item, is affected and add the products, we will have 
the percentage of the average cost of a train-mile which 
shows the effect of one mile of such change in alinement. 
If we multiply this percentage by the average cost of a 
train-mile, we will then have the cost for each train-mile 
operated of so much change in alinement. Multiplying 
that value by the number of trains run per day or per year, 
we will then have the daily or annual cost of that change 
of alinement for that road. If, for example, we find that 
a certain change in alinement would make a saving of 
24 c. for each train passing over the road, then the annual 
saving, if there were 3000 trains per year, would be $720. 
But an annual saving of $720 would justif}^ the expendi- 
ture of $14,400 if interest were at 5%. If, therefore, the 
change can be made for an expenditure of about $14,000, 
it will probably be justified. 

73. Reliability of such estimates. — It may be argued that 
such calculations are utterly useless, because the data on 
which the computations are based are variable and to 
some extent non-computable, and therefore no dependence 
can be placed on the calculations. This is true to the 
extent that it is useless to claim any great precision in 



OPERATING EXPENSES. 107 

the computation of the value of any proposed change of 
alinement. In the numerical case suggested above it is 
assumed that the saving amounts to only $720 per year. 
The cost of making the change is very easily computed. 
If it is found that it can be done at a total expenditure of 
say $3000, then there is hardly any question of the advi- 
sability of making the change, for, with all the allowance 
which can reasonably be made in the method of computing 
the effect of the change, we can be sure that the final result 
is not in error by several times the true result. The 
question is not so much as to whether our computed 
capitalized value, $14,400, is mathematically precise or 
even correct to within 10%. The method of computa- 
tion gives a value which is fairly close and which will 
give a rational measure of the advisability of making the 
change. If the cost of the improvement very nearly 
equals the computed capitalized value, then it will probably 
make but little difference whether the improvement is 
made or not. Such a question would then depend more 
on the difficulty of raising money for the improvement. 
Also, if it is shown that the cost of making the improve- 
ment is far greater than the capitaUzed value of the im- 
provement as computed, then there is hardly any doubt 
that the improvement is not justifiable. 

To express the above question more generally, in every 
computation of the operating value of a proposed improve- 
ment, it may always be shown that the true value lies 
somewhere between some maximum and some minimum. 
Closer calculations and more reliable data will narrow 
the range between these extreme values. According as 
the interest on the cost of the proposed improvement is 
greater or less than the mean of these limits, we may 
judge of its advisability. The range of the limits shows 
the uncertainty. If it lies outside of the limits there is 
no uncertainty, assuming that the limits have been 



108 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

properly determined. If well within the Hm.its either 
decision will answer, unless other considerations determine 
the question. And so, although it is not often possible 
to obtain precise values, we may generally reach a con- 
clusion which is unquestionable. Even under the most 
unfavorable circumstances the computations, when made 
with the assistance of all the broad common sense and 
experience that can be brought to bear, will point to a 
decision which is much better than mere ^'judgment," 
which is responsible for very many glaring and costly 
railroad blunders. In short. Railroad Economics means 
the application of systematic methods of work plus 
experience and judgment rather than a dependence on 
judgment unsystematically formed. It makes no pretense 
to furnishing mechanical rules by which all railroad 
problems may be solved by any one, but it does give a 
general method of applying principles by which an engineer 
of experience and judgment can apply his knowledge to 
better advantage. To the engineer of limited experience 
the methods are invaluable; without such methods of 
work his opinions are practically worthless; with them his 
conclusions are frequently more sound than the unsystemat- 
ically formed judgments of a man with a ghttering record. 
But the engineer of great experience may use these methods 
to form the best opinions which are obtainable, for he can 
apply his experience to make any necessary local modifica- 
tions in the method of solution. The dangers lie in the 
extremes, either recklessly applying a rule on the basis 
of insufficient data to an unwarrantable extent, or, dis- 
gusted with such evident unrehability, neglecting alto- 
gether such systematic methods of work. 



CHAPTER VII. 

MOTIVE POWER. 

Economics of the Locomotive. 

74. Total cost of power by the use of locomotives. — 

The total cost of motive power by the use of locomotives 
must be determined by a consideration of the first cost of 
the locomotive, the cost of maintaining it in condition for 
work, and the cost of operating it. Considering the vari- 
able life of locomotives of different cost, we must con- 
sider, instead of the first cost of the locomotive, the average 
annual cost which will be the equivalent of the actual total 
cost through the period of the life of the locomotive. In 
general it may be said that the heavier and more expensive 
locomotives have been found most economical, consider- 
ing the ton-miles of hauling which they accomplish during 
their total life, than the lighter and less expensive loco- 
motives, but the economics of any type of locomotive can 
only be determined by a consideration of all the terms 
involved. As a general statement we may say that a 
locomotive *is the cheapest which will haul a ton-mile over 
any combination of grades and curves at a less total cost 
(considering all items) than will be charged to any other 
engine of its class. Strictly speaking, even the above test 
should be applied only to compare the locomotives of one 
class, and perhaps only to freight-locomotives. Passenger- 
locomotives usually have the requirement of high speed, 
which cannot be obtained except at a proportionate sac- 

109 



110 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

rifice in hauling capacity. But it is not even possible to 
consider that the test of any one locomotive will be an 
accurate measure of the efficiency of that type, since it is 
often found that locomotives, which are built at the same 
shop, according to identical plans and used in the same 
kind of service, will have a very different history regard- 
ing shop repairs, fuel and supphes consumed, etc. Of 
course there is a reason for this in each case, and the 
blame is ordinarily laid on the enginemen. \^T:iile this 
is frequently justifiable the engine-builder may also be 
somewhat to blame. A summation of the percentages of 
Items 12, 21, 22, 23, 24, and 25 in the classification of 
operating expenses, referred to in Chapter VI, show^s that 
the average for ten years is as follows : 

Table X. — Cost of Maintenance and Operation of Locomotives, 

1894-1904. 



Item 12 — Repairs and renewals of locomotives. . 
21 — Engine- and roundhouse-men — wages. 

22 — Fuel for locomotives 

23 — Water-supplies for locomotives 

24 — Oil, tallow, and waste for locomotives. 
25 — Other supplies for locomotives 



Percent- 


Cost in 


age of total 


cents per 


cost of a 


train-mile. 


train-mile. 




6.538 


6.983 


9.607 


10.260 


10.316 


11.019 


.047 


.692 


.377 


.403 


.202 


.216 



The average cost per train-mile for the same ten years 
equals 106.813 c. If we multiply these percentages by 
this average cost we obtain the average cost in cents per 
train-mile for these various items, as given in the last 
column of Table X. 

75. Renewals of locomotives. — If there were no varia- 
tions in the types and the cost of locomotives, as built 
from year to year, it would be comparatively simple to 
charge the entire cost of renewals as operating expenses; 



MOTIVE POWER. Ill 

but since there has been, and perhaps always will be, a 
development in the type of locomotive used, the newer 
being usually more costly, but in spite of their added cost 
being really more economical, we find that the cost of the 
new locomotives is constantly greater. The strictly proper 
method would be to charge up the excess cost of the new 
locomotive as an addition to the property of the road. 

There is quite a difference in the policies of roads, espe- 
cially when we compare the roads of this country and of 
England with respect to the character of work and mate- 
rials used. In general it may be said that the locomotives 
in England last many years longer than they do in this 
country, and that there are now some locomotives still in 
use which have been in service for forty or fifty years. In 
America the policy is different. An engine is built with 
the expectation that in twenty years or perhaps less it 
will be in the scrap-heap. While it is in service it is worked 
very hard, and its annual mileage is very much greater 
than the mileage of an English locomotive. By the time 
it is thrown into the scrap-heap it has a mileage perhaps 
greater than an English locomotive with twice its life. 
The locomotive is then replaced with a newer type which 
is more economical, while the English locomotive is per- 
haps considered too valuable to throw away, and is there- 
fore continued in service with less economy than would 
be obtained from a more modern engine. Of course the 
relative economy of these two methods may be open to 
discussion, but it is claimed that the American method of 
quickly obtaining the maximum of usefulness of a loco- 
motive and then throwing it away produces an actual 
economy in the cost per ton-mile. The comparison of the 
two methods is somewhat compHcated, owing to other 
conditions, such as cost of fuel, labor, etc., which would 
modify the apparent result and render the true result more 
uncertain. A. M Wellington stated several years ago that 



112 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

the average mileage life of English and European locomo- 
tives was about 450,000 to 500,000 miles, and at the same 
time gave the life of American locomotives as 700,000 
miles. The practice of railroads at the present time is to 
obtain a far higher railroad mileage, the mileage per year 
frequently amounting to 50,000, and records of 8000 to 
10,000 miles per month for several months are very com- 
mon with passenger-engines. If we consider that any 
given locomotive will have a life of twenty years and that 
its mileage per year will average 50,000 miles, thus making 
a total of 1,000,000 miles during its life, the railroad could 
create a fund by an annual payment which at compound 
interest would produce the total cost of renewing the 
locomotive at the end of twenty years, or at least of fur- 
nishing an amount equal to its present cost. Tables show 
us that 3 c. per year at compound interest for twenty 
years will produce $1, or, if we consider the cost of the 
locomotive as $10,000, $300 per year, compounded at 5%, 
will produce $10,000 at the end of twenty years. If the 
locomotive has an annual mileage at 50,000, we should 

$300 
charge rTw^, or 0.6 c. per mile as the item to take care 

of the regular renewals. Of course such items would only 
apply to the cost of renewing that engine with one of 
equal cost. The probabilities are that the new engine 
will actually cost more money. The economics of heavier 
engines will be discussed later. 

76. Repairs of locomotives. — The term ^^renewals of loco- 
motives^^ applies only to the literal substitution of a new 
locomotive for one which has been sent to the scrap-heap. 
Repairs are divided into two classes: general repairs and 
current repairs which are usually made in a roundhouse. 
The term '^general repairs" applies to the more expensive 
work of repairing which is done in one of the general repair- 
shops of the road rather than in the roundhouse. Some 



MOTIVE POWER. 113 

roads consider that the repairs to a locomotive should be 
considered as general repairs if the amount of work to be 
done at any one time exceeds a certain figure, say $750, 
but as such a method of classifying repairs is purely arbit- 
rary and depends to some extent on the amount of work 
that is done at the roundhouse in keeping the engine in 
condition, any comparison between the figures of two 
roads are almost useless. It is ordinarily expected that a 
passenger-locomotive should make 120,000 miles and a 
freight-engine 80,000 miles between consecutive assign- 
ments to the shop for general repairs, but even such figures 
are of little significance, except that, if a locomotive should 
be sent to the shop without having made some such mile- 
age since the last visit, it Vv^ould imply that there had been 
some mismanagement (barring accidents) for which some 
one was responsible. The term ^^ current repairs" includes 
all the smaller repairs which are not considered of suffi- 
cient importance to demand a general overhauling of the 
locomotive. The figures reported by various roads for the 
cost of current repairs per engine handled average some- 
thing over SI per engine. Taking the figures in connec- 
tion with the mileage -run it would show an average cost 
of from one to two cents per mile-run. Under very un- 
favorable conditions the total cost of general and current 
repairs may amount to from 10 to 15 c. per mile-run. Con- 
sidering the average figure for the country given in a 
previous section (Item 12, 6.983 c), if we deduct .6 c. 
(or even a little more) as the cost for renewals we have 
left about 6 c. as the total average cost of the country of 
the general repairs. This seems to agree very closely with 
the statistics given by a certain road that the average 
cost of engine repairs per freight-engine mile during a 
period of seven years varied from 5.88 to 6.82 c, or an 
average of 6.30 c. per freight-engine mile. Another road, 
which gives the cost of freight-engine repairs as 7.22 c, 



114 THE ECONOMICS OF RAILROAD CONSTRUCTION, 

per engine-mile, quoted at the same time the cost of 
passenger-engine repairs as 5.60 c. per engine-mile. If, 
however, we consider these figures on the basis of the work 
accomplished by the locomotives, we have another indica- 
tion of the large economy in the use of heavy engines 
hauling heavy trains. In the last-mentioned case the 
costs were 22.88 c. for passenger-engines and 7.73 c. for 
freight-engines per thousand ton-miles; but the freight- 
trains were more than four times as heavy as the passenger- 
trains, so that, although the freight-engines cost far more 
than the passenger-engines per engine-mile, the cost per 
ton-mile was far less. It is usually found that compound 
engines cost much more per engine-mile than simple 
engines of the same capacity, and that the comparison is 
made still worse because their annual mileage is apt to be 
less, owing to their standing so much time in the repair- 
shops. On account of the very great variety of engines, 
the cost of engine repairs per engine-mile is very different 
for different types of engines, and the cost per ton-mile 
is likewise very variable. Mr. G. R. Henderson has sug- 
gested that the cost of repairs may be represented by the 
very simple formula of 1 c. per ton of tractive force per 
mile plus 1 c. per engine-mile. In this statement, how- 
ever, he considers the term ^'tractive force" to be the 
average force which is actually exerted, and not the 
maximum tractive power. For example, he considered a 
passenger-engine, whose tractive force amounts to ten 
tons, and assumed that the actual tractive force exerted 
by it will not average more than 40% of this maximum. 
For the above case the assumed cost of repairs would be 
40% of 10 or 4X1 c. + l c. for each mile-run, making a 
total of 5 c. per mile. This method is applied to pusher- 
engine service as follows: He assumes an engine with 
40,000 pounds tractive force, which is exerted to its full 
capacity in running up-hill^ and which returns down the 



MOTIVE POWER. 115 

hill without the use of steam. Applying the principle to a 
grade twenty miles long, the item chargeable to repairs 
for the up-hill run would be 20X20 c. + 20 c. or $4.20. 
For the down-hill trip we would have merely 20X1 or 
20 c, making a total of $4.40 for the 40-mile round trip, or 
an average of 11 c. per mile. In the case of pusher service 
it is generally correct to assume that the engine is working 
to its full capacity in climbing the hill, and that it does 
not have to use steam in going down. When we apply 
such a formula to the undulating grades on an ordinary 
road, it becomes very difficult to determine the proportion 
of the total possible tractive force which is actually exerted. 
Usually we can only make a very approximate assumption. 
77. Wages of engine- and roundhouse -men. — Enginemen 
and- firemen are usually paid by the ^Hrip," a trip implying 
a distance of 100 miles. If a division happens to be 
somewhat less than 100 miles, it is usually considered to 
be 100 miles, and the men will be paid according to the 
number of ''trips" made per month. If the run is more 
than 100 miles a proportionate amount is usually added 
per trip. The wages paid, however, vary considerably, 
according to the tonnage of the engine, it being considered 
that the heavier engines require a better grade of service 
and possibly a more dangerous service. But, beside the 
regular schedule allowances paid for regular service, there 
is a specific allowance of 25 c. per hundred miles above 
the regular rate for way-freight trains. The enginemen 
for pusher-engines are paid for a day of 12 hours or less 
with some increased pay for overtime work. Switching 
enginemen are also paid by the day. Enginemen on 
engines running light are paid the same rate as those on 
passenger-engines. Enginemen are usually paid somewhat 
less during their first year of service as enginemen than 
they are during succeeding years. On one road, with a 
very complete schedule for payments of different kinds 



116 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

of service, all men with regular assignments are guaranteed 
2600 miles per month unless they are responsible for loss 
of time and mileage. The methods for allowing for over- 
time are quite varied. It is frequently specified that no 
overtime shall be allowed for enginemen in passenger service 
unless the time of the trip exceeds eight hours. For freight 
service the limit is made ten hours. This is practically 
on the basis of running a freight-train at an average speed 
between terminals of 10 miles per hour, assuming that 
the division is 100 miles long. In order to equalize the 
differences in the difficulty in handling trains on different 
divisions, due to various sources, such as extraordinarily 
heavy grades, etc., it is usual for the railroad companies 
to arbitrarily consider the division to have a certain 
number of miles somewhat in excess of the actual mileage. 
This increase is sometimes as much as 25% and must 
practically be considered as merely adding so much to the 
engineman's wages per mile, although the amount added 
is variable. There is also a very large amount of mileage 
added on many roads where the grades or the amount 
of traffic in opposite directions is very different, due 
to the amount of light-engine mileage. This applies 
particularly to freight service, although it may apply to 
some extent to passenger service. A consideration of 
the above data will show that the wages assignable to the 
enginemen for each mile actually run, and especially for 
a mile of distance which might be added or cut out, is 
very different from the average wages actually paid to 
them. The average daily compensation actually paid to 
enginemen and firemen in the different parts of the United 
States during the year 1904, as compiled by the Interstate 
Commerce Commission, has already been given in § 62. 
The average percentage of operating expenses assignable 
to enginemen and roundhouse-men for the year 1904 was 
9.386%. Multiplying this by the average cost of a train- 



MOTIVE POWER. 117 

mile for the same year (131.375 c), we have 12.331 c. per 
mile. This expense represents the tot/al assignable to the 
three classes of enginemen, firemen and roundhouse- 
men. The term ''roundhouse-men" here includes hostlers, 
wipers, oilers, cleaners, ash-pit men, dispatchers, call-boys, 
general roundhouse-men, and men employed in the super- 
intendence of the roundhouse. The actual per-diem wages 
paid them is of course variable. The total amounts 
paid in 1904 to each of these three classes (engineers, 
firemen, and roundhouse-men) were $68,946,543, $40,463,- 
040, and $16,031,241 respectively. The percentages of 
these subitems to the total item are 54.97c, 32.3%, and 
12.8% respectively. Multiplying these first two percent- 
ages by the total cost of the item in cents per train-mile, 
we have average figures for the wages paid to enginemen 
and firemen per train-mile, which are 6.78 c. and 3.98 c. 
respectively. As a matter of fact, the average compen- 
sation paid per actual mile traveled is far greater than 
this, on account of the excess allowed to these men for 
overtime, constructive mileage, etc., which is almost 
invariably compensated for to the advantage of the men 
rather than to the company. For example, if a freight- 
train is delayed for several hours, the men are paid for 
their time (whatever may be the basis), while the delay 
is an absolute loss to the company. 

78. Fuel for locomotives. — It should not be forgotten 
that the cost of fuel per ton at the mine, or even the cost 
when delivered at the coaling-stations, is by no means the 
measure of the economy in fuel. The value of fuel per ton 
depends on its heating capacity, and varies from the value 
of wood (which is still used in some places where it is ex- 
ceptionally cheap) as fuel, up through various grades of coal 
to the use of oil, which furnishes more heat per ton than 
any other grade of fuel. For general use we may ignore 
these two extremes, since in nearly all localities wood for 



118 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

fuel is not only costly, but of comparatively little value. 
At the other extreme, oil for fuel is almost impracticable, 
except where the Texas oils, whose composition gives 
them a particularly high fuel value, are sufficiently con- 
venient to make their use economical. One ton of fuel- 
oil has a heat equal to about IJ tons of good coal or two 
tons of lignite. The saving in hauling of fuel, the ability 
to regulate the firing so as to produce a uniform heat, 
the actual saving in repairs to the fire-box, the utter 
absence of expenses incident to ash-handling plants, com- 
bine to give this method an economy which is even greater 
than would have been indicated by the comparative cost 
in cents of evaporating 100 pounds of water. 

It sometimes happens that it will pay to haul coal from 
a more distant source, considering the price which is paid 
for it, rather than use a coal which is mined much nearer, 
because the actual amount of ton-miles of energy pro- 
duced may be greater with the more expensive coal. For 
example, the values of different fuels have been carefully 
determined and classified according to the number of 
ton-miles which can be obtained per pound of coal. A 
few of these values, which, however, must be considered 
as average values, are as follows: 7.00 for Pennsylvania 
anthracite, West Virginia New River semi-bituminous, 
and cannel coal; 4.35 for Iowa lignite, and 4.25 for 
Colorado lignite slack. After all, the real question is to 
determine how to get the most heat for an expenditure 
of $1.00 at the coaling-stations. Since the cost of haul- 
ing must be included, any set of values made out for 
one locality are almost worthless for any other locality. 
As an example, a few values are extracted from some 
computations made by W. H. Bryan as to the real value 
of three grades of coal in St. Louis. 

It may be observed from the following tabular form 
that for a coaling-station located at St. Louis the common 



MOTn^ POWER. 



119 



Kind of coal. 


Cost per ton. 


B. T. U.in 
one pound. 


Cost of evap- 
orating 100 
lbs. ot water. 


Anthracite 


$6.75 

4,75 

.90 


14,000 
12,500 
10,000 


31.8 c. 


Pocahontas bituminous 

Common slack 


24.87 
7 25 







slack obtainable in that locality is by far the cheapest 
coal to use, regardless of its cost per ton. There is one 
slight compensation which reduces the apparent disad- 
vantage of these figures. The anthracite coal will pro- 
duce 40% more heat per pound than the common slack, 
and therefore the expense of hauling the extra weight of 
slack in order to produce a given amount of energy from 
the coal, as well as the necessity for re-coaling more 
frequently with the cheaper grade of coal, gives the 
anthracite coal an advantage which would make it the 
more economical coal if the values given in the last column 
were equal or nearly so. Of course in the above case 
those advantages are utterly swallowed up by the cheap- 
ness of the common slack. 

In computing the real cost to a railroad of the fuel which 
it uses, the cost of the coal to the point where it is deliv- 
ered to the road from another railroad is but an item of 
the total. There must be added to this the real cost to 
the road of hauling it from the point of delivery to the 
various coaling-stations. The actual cost of this will of 
course vary with the different roads, but it will seldom be 
less than J c. per ton-mile, which is the same as adding 
50 c. per ton to the cost of the coal for each hundred 
miles it is hauled from the point of delivery. 

Handling the coal at the coaling-station adds another 
item to its real cost to the road. The old-fashioned 
method of shoveling from a coal-car to a platform or bin, 
and from there again shoveling into a tender, will add 
at least 25 c. per ton to the cost of coal. The various 



120 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

devices for handling coal cheaply, although they reduce 
the cost of handling the coal, add an interest charge to 
pay for a more or less expensive coal-handling plant. 
The cost of handling coal by means of the modern coaling- 
station will usually average 3 c. per ton, and it is easily 
demonstrable that such a method is economical even to 
the point of paying the interest and maintenance on the 
cost of the plant, provided the business of the road is 
sufficiently large to justify such a plant. 

79. Water-supply — impurities. — The desired qualities in 
the water-supply must be the first consideration. While 
in general it may be said that water which is suitable for 
drinking purposes is suitable for locomotive-boilers, even 
this statement cannot be taken absolutely. A catalogue 
of the desired qualities in the water-supply can best be 
stated by describing the objectionable qualities. It is 
popularly supposed that an absolutely pure distilled water 
would be the ideal type of water to use. Apart from the 
high cost of distillation, distilled water is actually objection- 
able, since it attacks the iron of the boiler quite rapidly 
and causes it to rust. The purer the water the more 
quickly will it attack the iron. A second objectionable 
quality of water is that caused by the presence of carbonates 
of lime or magnesia. When water containing these car- 
bonates is boiled, the carbonates are deposited on the 
surface of the boiler, and since they are poor conductors 
of heat, the efficiency of the boiler is reduced on account 
of the lack of heat-conductivity of the scale. This form 
of scale, however, is not hard and is readily washed out, 
but such impurities in the water cause trouble and expense 
in proportion to the amount of them. The sulphates of 
lime and magnesia are far more dangerous. They deposit 
on the surface of the boiler in a very hard scale, which 
is removed with great difficulty. The difficulty of remov- 
ing them may cause the washing-out process to be ineffec- 



MOTIVE POWER. 121 

tivc, unless very thorough, and the hard scale may be 
allowed to accumulate until it becomes very thick. In such 
a case the situation becomes actually dangerous, since the 
scale is a very poor conductor of heat. Since the intense 
heat of the fire is not readily transferred to the water, 
the iron will become overheated until it may actually 
soften and give way, causing an explosion. The dangerous 
effect of such water, and the great difficulty of removing the 
scale formed by these sulphates, render such waters very 
undesirable. 

Water sometimes contains sulphuric acid, especially if 
it has drained out of a coal-mine. Other acids may occa- 
sionally be found, owing to the contamination of the source 
of supply by some industrial works. These acids will 
corrode the iron in the boiler and soon cause deterioration. 

One of the most common difficulties with boiler-water 
is that caused by the presence of the sulphate or chloride 
of sodium or the chloride of calcium. The presence of 
these chemicals produces what is known as ^^ foaming." 
Although the steam-pipe running from the boiler to the 
cylinder is led from the dome of the boiler, which is pur- 
posely made as high as possible above the surface of the 
water, the foaming of the water will carry more or less 
liquid water into the steam-pipe and from thence to the 
cylinders. This results in broken cylinder-heads and 
pistons, broken valves, and many forms of destruction of 
the machinery. To avoid this effect when using foaming 
water, the engineer or fireman will keep the water as low 
in the boiler as he dares, in order that the surface of the 
water shall be as far as possible below the dome. In the 
endeavor to accomplish this, too little water may be left 
over the crown-sheet, which becomes overheated, and the 
fire-box is ruined even if the boiler does not explode. 

On account of the many evils resulting from impurities, 
as described above, railroads now generally follow the 



122 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

policy of submitting all proposed sources of water to a 
thorough chemical analysis, in order to determine their 
qualities. The actual evils resulting from the use of 
impure water, which show themselves in the expense 
accounts in excessive repair charges for the repairs of 
boilers, fire-boxes, leaky tubes, with an occasional boiler 
explosion, justify the expenditure of considerable sums 
of money to obtain suitable water-supplies. The very 
large increase in recent years in the number of small mu- 
nicipalities which have constructed water-works for their 
own use, has resulted in many railroads relying on such 
water-supplies for the supply of their local water-stations. 
Although it is generally possible to obtain by pumping 
from a private w^ell or a stream a sufficient quantity of 
water at a much lower price per gallon than would usually 
be charged by the municipality, nevertheless it is generally 
advisable, especially in view of the danger of the future 
contamination of a well or stream, which may at th 
present give a suitable supply, to utilize these municipal 
supplies. 

The above paragraphs describe the evils of a contam- 
inated water-supply. The requirements of operation, 
which necessitate the location of water-stations at approx- 
imately fixed places on the line of the road, leave no 
alternative but to use such water as is obtainable and, if 
necessary, to treat it chemically before it is used, so that 
it will not be injurious. In the early history of the South- 
ern Pacific Railroad there were stretches of several hundred 
miles where water was unobtainable, or else was so alka- 
line as to be unfit for use. For a considerable time after 
the road was built it was considered necessary to haul with 
each train one or two large tank-cars carrying water in 
order to supplement the supply carried in the tender. 
Later the same railroad incurred considerable expense, 
after seeking the most expert geological advice obtainable 



MOTIVE POWER. 123 

on the probabilities of obtaining water by sinking Artesian 
wells, and thereby succeeded in locating water-stations 
approximately where they were desired by the operating 
conditions. In ordinary cases a comparatively simple 
treatment of the water with chemicals will so modify the 
injurious ingredients that they are virtually rendered 
harmless, so far as boiler use is concerned, although the 
water is still very far from being pure water. Of course 
the method of treatment depends entirely on the nature 
of the chemical present in the water. A treatment suit- 
able for one kind of water would only render another kind 
of water still more harmful. 

80. Methods of water purification. — One of the cheapest 
methods is to introduce a chemical directly into the tender- 
tanks. From here it passes to the boiler. Even this 
method is only suitable when the resulting precipitate 
will not cause a scale to form on the boiler-shell. At its 
best it requires frequent washing-out of the boiler. Such 
a method qannot be considered good practice, even though 
it is cheap. 

When the impurities in the water consist chiefly of the 
carbonates of lime or magnesia which are held in solution, 
the treatment is very simple and inexpensive. These car- 
bonates are only held in solution as long as the water is 
charged with carbonic-acid gas, as it always is under 
these conditions. If common lime is thrown into the 
water it unites with the free carbonic-acid gas and absorbs 
it. Since these carbonates are insoluble in water which 
is free from carbonic-acid gas, they are precipitated and 
the clear water may then be drawn off. The lime required 
for a water containing 40 grains of carbonates per gallon 
will cost less than one cent per thousand gallons. The 
cost of the labor may be more than this. A very few cents 
per thousand gallons will usually suffice for the cost of 
such purification. When the sulphate of magnesia is 



124 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

present the purifying is far more expensive, since it 
requires the use of sodium carbonate or '^ soda-ash" as 
a reagent. This is worth about one cent per pound, and 
the cost of the required amount for 1000 gallons will be 
about one cent for each eight grains of sulphate per gallon. 
Sometimes the water is so strongly impregnated that a 
very large amount of reagent is necessary, and the resultant 
water may become objectionable on account of '^ foaming." 

A complete study of the precise chemical character of 
the water, together with the amount and cost of the neces- 
sary reagents, is the only wise method to pursue even 
before any source of supply is selected. Railroads have 
frequently found it wise to abandon sources of supply on 
which considerable money has already been spent, because 
it has been discovered that the water was selected without 
a proper appreciation of its disadvantages. 

8 1. Pumping water. — The maintenance of water in the 
tanks is accomplished chiefly in one of four ways: (1) 
gravity, which is imipossible or impracticable, except under 
peculiarly favorable conditions; (2) by windmills, which 
are too uncertain, unless an extra-large storage capacity 
is provided, which reduces the economy of the method; 
(3) by steam-engines; and (4) by gasohne-engines. The 
first two methods need hardly be discussed. Under espe- 
cially favorable circumstances they have their advantages 
of economy of maintenance if not of first cost. The 
methods of direct engine-pumping are the only standard 
methods which are everywhere applicable. The develop- 
ment of gasoline-engines during the last few years has 
resulted in a very large increase in the use of engines of 
this type. The great advantages of the gasoline-engine 
type are due to the low cost of the gasoline, which is usually 
not more than 10 c. per gallon, and, secondly, the facility 
with which the engines are run, even by a very low grade 
of unskilled labor. The economy is even greater when the 



MOTIVE POWER. 125 

size of the plant is very small, since very small steam- 
engines will use as much as 15 or 20 pounds of coal per 
horse-power hour. Under similar conditions a gasoline- 
engine will use about one-tenth of a gallon. Some com- 
parative estimates made by the Chicago & Alton Railroad 
at several places found that the cost of pumping (using 
coal) was anywhere from 1.4 to 3.4 times as great as the 
cost when using gasoline. Of course the absolute cost 
per thousand gallons depends very largely on the height 
to which the water must be raised, as well as on the size 
of the plant, but in round numbers it may be said that the 
cost of pumping water per thousand gallons by steam will 
vary from 4 to 10 c. per thousand gallons, while the 
cost using gasoline will vary from IJ to 3 c. 

82. Oil, tallow, and waste for locomotives. — These are 
quoted for the whole United States at an average price 
of .403 c. per train-mile, but it should of course be remem- 
bered that this figure is only an average figure which will 
be increased or diminished very largely in individual cases. 
Of course the cost is greater for heavier engines and 
heavier trains. The proportion of the item which should 
be assigned to the cars, which is perhaps not more than 
50%, will probabl}^ vary nearly according to the nmnber 
of cars per train. The cost per engine-mile varies with 
the size of the engine, and will be far cheaper per ton-mile 
for the heavier engines than for the lighter engines. The 
cost of this item for engines alone seems to vary from 
.15 c. per engine-mile for a very light passenger-engine 
up to .30 c. for a very heavy freight-engine. On the 
other hand, it was found from some figures compiled on 
the A. T: & S. F. R.R., that for two engines with loads 
behind them of 702 and 416 tons respectively, the cost of 
the oil and waste per mile was .28 and .24 c, but if we 
reduce these figures to the cost per thousand ton-miles, 
the cost was .40 and .58 c. respectively. Both wool- 



126 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

waste and cotton-waste are used, the wool-waste costing 
from 50 to 100 per cent more than the cotton-waste. 
The wool-waste is better for the cellar of a driving-box, 
since it is more elastic and will therefore stand up better 
against the under side of the axle. Cotton-waste is even 
better for the tops of journal-boxes, as it lies flatter and 
heavier, and therefore prevents the dust from getting on 
to the bearings. Tallow is also used for such purposes 
and is far cheaper than waste. This item is so very small 
that we may usually neglect any variations in the amount 
of it, except when we are considering the economics of 
heavy engines vs. light engines, and then the difference is 
worth considering. 

Other supplies for locomotives include the tools, the 
sand, and all miscellaneous articles, such as metal polish, 
torpedoes, etc. Under the head of tools it includes oil- 
cans, lanterns, scoops, fire-bars, torches, etc. The cost of 
these items averages about .2 c. per train-mile, although 
the figure may vary 50% each way. 

83. Comparative cost of various types of locomotives. 
— In Table XI are given the comparative costs of the 
various sizes of standard-gauge locomotives, the figures 
having been furnished through the courtesy of the Baldwin 
Locomotive Works. While these figures must be con- 
sidered approximate, since the actual cost of a locomotive 
depends somewhat on the particular kinds of attachments 
which are used, the table has its value in indicating to an 
engineer the approximate cost of the desired equipment 
for a new road, and also shows the comparative costs of 
the various types of engines. The last column is particu- 
larly instructive, since it indicates the great economy of 
the Mogul type, and even more so of the Consolidation 
type, where the maximum of tractive power, rather than 
high speed, is the prime consideration. The table refers 
exclusively to simple locomotives. As a very approximate 



MOTIVE POWER. 



127 



figure it may be stated that the cost of building any of 
these locomotives on the compound type will be approxi- 
mately $2500 more than that of the corresponding simple 
type. 

Table XL — Comparative Cost of Various Sizes of Standard-gauge 
Simple Locomotives. Baldwin Locomotive Works. 

AMERICAN type. 





Weight (net tons). 




Cost, 


1906. 




Cylinders. 




On 








Per ton on 




Total. 


driving- 
wheels. 


Total. 


Engine. 


Tender. 


driving- 
wheels. 


12''X22'' 


25 


16 


$6,800 


$5,600 


$1200 


$425 


13''X22'' 


30 


19 


7,200 


5,950 


1250 


379 


14''X22'' 


37.5 


23.5 


7,600 


6,300 


1300 


323 


iy'X24'' 


42.5 


27.5 


8,100 


6,700 


1400 


294 


16''X24'' 


46 


30 


8,600 


7,100 


1500 


287 


17''X24'' 


50 


33 


9,200 


7,650 


1550 


278 


18''X24'' 


55 


36 


9,800 


8,200 


1600 


272 



mogul type. 



16''X24'' 


45 


39 


$8,700 


$7,400 


$1300 


$223 


17''X24'' 


50 


42.5 


' 9,400 


8,050 


1350 


221 


18''X24'' 


53.5 


45.5 


10,000 


8,550 


1450 


219 


19''X26'' 


60 


51 


10,600 


9,000 


1600 


208 



CONSOLIDATION TYPE. 



20''X24'' 
2r'X26'' 

22''X28'' 


69 

82.5 
95 


61.5 
75 

85 


$12,600 
13,400 
15,000 


$11,000 
11,650 
13,250 


$1600 
1750 
1750 


$205 
179 
176 



The Economics of Heavy Locomotives. 

84. The problem stated. — A heavy locomotive costs con- 
siderably more than a light locomotive. A heavy locomotive 
costs more to operate, will burn more fuel, use up more 
water, lubricants, and other supplies. The heavier engine 
will cause more damage to the road-bed and will produce 



128 THE ECONOIVIICS OF RAILROAD CONSTRUCTION. 

greater wear on the rails and ties. On the other hand, the 
wages paid to the enginemen, although somewhat greater 
on heavier locomotives, do not increase in proportion to 
the tonnage. The hauling capacity of the engine is far 
greater and the operating cost per ton-miie is far less. 
The introduction of air-brakes on all passenger-trains and 
on freight-trains to a sufficient extent to permit the 
engineer to handle the train, without the use of brakem^-n 
working hand-brakes, reduces the proportion of brakemen 
per car, or, in other words, increases the number of cars 
to one brakeman, and therefore decreases the cost per 
car or per ton-mile for train service. It is comparatively 
easy to demonstrate that the cost per ton-mile of handling 
the trains by means of heavy engines is less than the 
cost when using light engines. The precise determina- 
tion of such economy is far more difficult, and must of 
course be considered to some extent uncertain. It is 
not a very difficult matter on any one road to determine 
the relative cost of operating two types of engines, one of 
which can haul 60 to 70% or even 100% more cars than 
another. But even after such calculations are made the 
results have only a general value, since they apply only 
to those two types of engines. Of course such comparative 
figures will have their value to the railroad manager who 
is considering the policy of renewing or substituting for 
his old light-weight locomotives a far heavier type of 
locomotive, and who wishes to justify the additional 
expenditure for the heavier locomotives by a demonstra- 
tion of the economy that would be obtained by using it. 
Perhaps the most simple method of making the calcu- 
lation is to consider the value of the substitution on the 
basis of the number of trains that would be thereby saved 
in handling a given amount of traffic. It may readily 
be appreciated that the gross amount received by a rail- 
road company for handling a certain gross tonnage of 



MOTIVE POWER. 129 

freight is a perfectly definite figure, which is neither in- 
creased nor diminished whether it is handled in four, six, 
or eight train-loads. If the manager can demonstrate 
that by the substitution of heavier locomotives a certain 
gross tonnage of freight can be handled in one or two less 
trains than would be required by the lighter locomotives, 
it is only necessary to compute the saving by running a 
less number of heavier trains, and then he has a basis on 
which to determine the justification of the added cost of 
his heavier locomotives. 

85. Economy efiected by handling a given traffic with 
one less train .^The general method adopted in this con- 
nection will be to consider the percentages of the various 
items of cost of a train-mile as given in Chapter VI, and 
to estimate the effect of the special circumstances of the 
problem on each one of these subitems. If the relative 
power of the two types of locomotives considered is such 
that the heavier locomotives can haul in three trains as 
many loaded cars as those of the lighter type would handle 
in four trains, or if the heavier engines handle in four 
trains as many cars as would require five trains with 
lighter engines, then the use of the heavier engines will 
save one train in four or one train in five, as the case may 
be. We will therefore compute the added cost of running 
the extra train. We may also consider this cost to be 
the same as the saving by avoiding the extra train, but, 
since the number of cars remains the same, we may con- 
sider that the total added cost is the cost of running say 
four engines instead of three. Of course, this does not 
mean the cost of running the additional engine ^' light." 
In the case here considered the gross tonnage of freight 
to be handled is assumed to be constant. We will there- 
fore assume that the total number of cars used in handling 
the freight is identical. We may therefore assume that 
the effect of these cars on the wear and tear of the track 



130 THE ECONOMICS OF RAILROAD CONSTRUCTION 

(Item 1) will be constant. It has been estimated that 
locomotives are responsible for approximately 50% of the 
general track-wear, on account of the greater concentration 
of loads on the driving-wheels. In recent years the wheel- 
loads of the heaviest freight-cars are as great as, or greater 
than, the driving-wheel loads of a few years ago, but the 
driving-wheel loads have also increased, although not in as 
great proportion. Although the disparity between driving- 
wheel loads and car-wheel loads is not now as great as it 
was twenty years ago, it is still sufficiently great, so that 
we may assume that 50% of the damage is the result of 
the wear due to locomotives. 

86. Maintenance of way. — The analysis of the subitems 
of Item 1, repairs of roadway, in Chapter VI, shows that 
a very large proportion of them are wholly independent 
of the tonnage or exact number of trains. It is safe to 
say that not more than 25% of the cost of track-labor 
will be influenced by the addition or reduction of a single 
train. If, therefore, we consider the engine to be respon- 
sible for 50% of the damage, we can add 50% of 25%, 
or 12^%, for the additional cost due to the extra engine. 
The renewal of rails and the renewal of ties will probably 
vary much more nearly in proportion to the number 
of trains. If we were to consider that repairs of roadway 
were strictly according to the tonnage, then there would 
be but little difference between the two systems of running 
four trains or three, since if the tractive powers of the 
engines were as 3 to 4, the weights of the engines would 
be approximately in the same ratio; but experience shows 
that the expenses of repairs of roadway have a singular 
uniformity per train-mile, regardless of whether the traffic 
is light or heavy. In the face of this, it is impossible to 
say that, since the gross tonnage would be nearly the same 
by both systems, we should consider that track repairs 
would likewise be the same for either system of operating. 



MOTIVE POWER. 131 

It is probably conservative to say that the running of 4 
trains instead of 3 will add 50% of the average cost of a 
train-mile to these two items. 

The repairs and renewals of bridges and culverts (Item 
4) will only be affected to the extent that the repairs 
of truss-bridges will evidently depend somewhat on the 
tonnage. The proportion of truss-bridges and of stone 
arches would evidently have an effect on this item, but 
it is so small that the uncertainty is of but little impor- 
tance. On the one hand, we might say that the deteriora- 
tion of truss-bridges would be increased by the heavier 
gross train-load, and especially by the heavier engines; 
but, on the other hand, as in the above item, the repairs 
have some relation to the number of trains. We will 
therefore consider the item as balanced, and the net 
effect zero. The other items of maintenance of way can 
hardly be said to be affected by the number of trains, 
except a possible addition of an insignificant amount to 
the item for buildings, due to the care of the extra engine 
in the engine-house. 

87. Maintenance of equipment. — Under the items of 
maintenance of equipment, the repairs of locomotives 
(Item 12) is the first important item to consider. The 
real question regarding this item is. Will the cost of en- 
gine repairs on four light engines be greater than on 
the three heavier engines which will do the same work? 
If we apply the rule that the cost of engine repairs equals 
1 c. per ton of average tractive force per mile, plus 1 c. 
per engine-mile, we will find, since the sum of the tons of 
tractive force required to haul the total tonnage of cars 
must be considered the same, that part of the item will 
balance. The other part of the item of repairs will vary 
according to the number of engine-miles; but the total 
item consists partly of the cost of renewals, and, since we 
may assume that the cost of the four Hght engines is nearly 



132 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

the same as that of three heavier engines, we may con- 
sider that the part of the item which has to do with 
renewals balances. Evidently no one figure will be a cor- 
rect answer for every case, but the method may be indi- 
cated as follows: Assume that we are comparing two types 
of engines, one of them having a tractive force of 15 tons 
and the other a tractive force of 20 tons. Then four of 
the lighter engines will be required to haul the same 
load which can be hauled by three of the heavier engines. 
Assume that an average of 50% of the maximum trac- 
tive force is utilized for the entire trip. Then accord- 
ing to the rule the cost of repairs for the three heavy' 
engines would be (.50x20)3+3 and for the light engines 
(.50x15)4 + 4, or 33 c. and 34 c. per mile respectively. 
It should be noted that, under the assumptions made, 
the largest part of the above items are identical for the 
two cases, and that the difference is very small. In fact, 
the difference is probably smaller than the probable error 
of the method of computation, and therefore we can 
probably say that, so far as Item 12 is concerned, the 
additional cost for engine repairs of using one additional 
locomotive to do the work, or the saving accomplished by 
using the heavier locomotive, will be practically zero. 

When we consider the repairs to the rolling-stock, we 
have an actual advantage in using light engines, since the 
average draw-bar pulls with the lighter train and the 
impact due to sudden stoppage is less, and, although 
some of the items of repairs will evidently be un- 
affected, none of them will be increased. The amount 
which they can be decreased is almost non-computable, 
since it depends on circumstances which in general can- 
not be foreseen. If the particular question involved 
concerns only the use of freight-locomotives, then we 
must ignore Item 13, the repairs of passenger-cars. It 
we analyze the cost of repairs of freight-cars, and consider 



MOTIVE POWER. 13'3 

that a very large proportion of them are clue to causes 
which have nothing to do with this question, we can see 
the justification of the estimate which has been made, 
that the cost of repairs of freight-cars may be reduced 
10% by the adoption of a greater number of trains to 
handle a given traffic. Even though this estimate may 
be considered as guesswork, it is quite evident that its 
error cannot be a very large percentage of itself, and it is 
quite certain that the error is only a very small percentage 
of the total quantity which we are trying to compute. 
Items 15 to 19 are unaffected by this question. 

88. Conducting transportation. — Item 20, superintend- 
ence, which includes only the salaries of higher trans- 
portation officials, may be considered to be unaffected. 
Item 21, the wages of enginemen, although they vary 
somewhat with the tonnage of the locomotives, do not 
vary in strict proportion to it. Some schedules of wages 
pay no attention to the weights of locomotives, but only 
consider the class of service, whether passenger service, 
through-freight, or local freight. In such cases the amount 
paid in wages would be strictly according to the number 
of engines. In other cases there is an addition of 5 to 
10% paid for handling the heavier engines. Assuming an 
average of 8% increase, we would have for four light engines 
400% and for three heavy engines 324%, or an addition of 
76% of the average wages for one engine, as the result of 
using the additional engine. Of course this item will 
vary with each particular case. The relative cost of 
fuel consumption with the heavier engines depends very 
largely on the particular engines compared. It is not 
unknown that a considerably heavier engine of one type 
may actually burn less fuel than a lighter engine of another 
type and make. When we consider the very large amount 
of fuel which goes to waste by radiation, the amount 
which is consumed when an engine is doing very little 



134 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

or no work, as when it is running on a level or on a down 
grade, and the proportion which is consumed in various 
other ways, as has already been described, it may readily 
be seen that only a small proportion of the fuel used may 
be considered as proportionate to its tonnage or propor- 
tionate to the weight on the drivers. The late A. M. 
Wellington considered that 75% of the fuel used would 
be unaffected by the weight of the engine, and that only 
the remaining 25% would be affected according to the 
tonnage. We might therefore express the amount of 
fuel used by four light engines as 

4X75% + 4X25%^400%. 

The cost of operating three heavy engines may be expressed 
as 

3x75% + 3(tx25%)=325%. 

Therefore the added cost of fuel for the one lighter engine 
would be 75% of the average figure for one. We will con- 
sider that the other engine-supplies are affected similarly. 
Items 26 to 32 may be considered as being strictly pro- 
portional to the number of trains, and therefore that the 
addition of an extra train will add 100%. We will con- 
sider the item of car-mileage as being unaffected. Items 
34 to 37, damages, etc., will be considered as being affected 
100%. The miscellaneous items^ 38 to 44, will in general 
be unaffected. Items 45 and 46 will probably be affected 
somewhat, although it is impossible to say how much. 
The items fortunately are so small that it will make but 
little difference what percentage is chosen. It will prob- 
ably lead to no material error to say that these items will 
be affected 50%. The general expenses. Items 47 to 53, 
will evidently be unaffected. If we multiply the normal 
average percentages, as given in Table IX, for the last ten 
years by the percentages which have been estimated for 



MOTIVE POWER. 



135 



each item, the summation of these products will be the 
percentage of the average cost of a train-mile, which will 
be an estimate of the cost of the assumed condition. If 
we multiply this by the average actual cost of a train-mile 



Table XII. — Additional Cost of Operating a Given Freight Ton- 
nage WITH Four Light Engines instead of Three Heavier 
Engines. 



No. 


Item (abbreviated). 


Normal 
average, 
per cent. 


Per cent 
affected. 


Cost 
per cent. 


1 


Roadwav 


10.767 
1.422 
2.948 
2.461 
3.436 


12.5 

50 

50 



0. 


1.346 


2 


Rails 


.711 


3 


Ties 


1.474 


4 
5 10 


Bridges and culverts 

Buildinsfs etc 


0. 
0. 










Maintenance of way 


21.034 




3.531 


11 




.617 
6.538 
2.174 
7.160 
1.535 


0. 
0. 
0. 
-10 
0. 


0. 


12 

13 

14 

15-19 


Repairs of locomotives. . . . 
* ' " passenger-cars. . . 
" " freight-cars 


0. 
0. 

-.716 
0. 










Maintenance of equipment. 


18.024 




-.716 


20 


Superintendence 


1.757 
9.607 
11.542 
23.149 
1.829 
2.288 
5.307 
1.157 


0. 

76 

75 

100. 

0. 

100. 

0. 

50. 


0. 


21 




7.301 


22-25 


Fuel, etc 


8.656 


26-32 
33 


Train-service, etc 

Car-mileage 


23.149 
0. 


34-37 


Damages, etc 


2.288 


38-44 


Miscellaneous 


0. 


45-4C 




578 










Conducting transportation 


56 . 636 




41.972 


47-53 


General expenses. 


4.305 


0. 















100.000 




44.787 



W3 v/ill have an estimate of the cost of one mile of this 
sort of operation. It is a question whether we should 
take the average figures for the last ten years, or the 
average figure for the last year alone, or, perhaps, even a 



136 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

still higher figure. As is indicated by Tables VII and IX 
and Fig. 6, the average cost per train-mile seems to be 
steadily increasing, while certain of the percentages of the 
items of cost seem to be regularly increasing (or diminish- 
ing) instead of merely fluctuating. On this account the 
averages for the past ten years will probably be incorrect 
as an estimate for immediate future costs. These per- 
centages have been combined in Table XII, page 135. 
If we assume that the average cost of a train-mile is $1.30, 
then the operating value of saving the use of the addi- 
tional engine equals 45% of $1.30 or 58 c. There is, how- 
ever, one additional item to be considered. Although Item 
12 includes repairs and renewals of locomotives, it does 
not include the addition, if any, for the capital cost of the 
extra locomotive. Perhaps this extra cost may be zero. 
If we consider that the cost of locomotives is roughly pro- 
portional to their tonnage, and that, with locomotives of 
the same type, the tractive force is nearly proportional 
to their tonnage, then the four locomotives would cost no 
more than the three heavier locomotives of equal power. 
But if the four locomotives cost somewhat more (as is 
probable), then the extra cost, say $2000, divided by the 
mileage life of the locomotive, say 800,000 miles, would 
require 0.25 c. to be charged to the above cost per mile. 
In this case the addition is almost too small for considera- 
tion, but in other cases it should not be neglected. 

89. Numerical illustration. — Assume that the general 
manager of a road is considering the justification of em- 
ploying heavier locomotives to handle a given tonnage. 
Let us assume that he can depend on a daily traffic which 
will fill 120 cars per day, having an average gross weight 
of 70 tons per car. This gives a total weight behind the 
tender of 8400 tons. A locomotive with a tractive force 
of 30,000 pounds would probably have a total weight of 
about 140 tons. When the tractive resistance on the 



MOTIVE POWER. 137 

level is six pounds per ton, the total grade resistance on 
a grade of 35 feet per mile is about 19.5 pounds per ton. 
If we have a tractive force of 30,000 pounds this would 
permit the hauling of trains with a gross load of 1540 tons. 
Subtracting the weight of the engine and tender, about 
140 tons, we would have 1400 tons as the permissible 
weight of cars behind one engine. This will permit the 
total tonnage to be handled in six trains with this type of 
engine. To handle this same tonnage in five trains in- 
stead of six will require a load of 1680 tons behind each 
engine. Assume that the heavier engines have the same 
ratio of tractive power to total weight, which is about 
10.7%. On this basis, letting W equal the weight of the 
locomotive in tons, we may say that (1680 + TF) 19.5 
=2000FX.107. Solving this for W, we find that the 
weight of the locomotive would be 168.4 tons, or about 
337,800 pounds. We would then have as the cost of 
handhng that traffic in five trains, five times SI. 30, or 
$6.50, for each mile of the road. Handling the traffic in 
six Hghter trains with lighter engines will cost a somewhat 
less price per train-mile, which may be expressed by the 
figure of five times $1.30 for five trains and 58 c. for the 
sixth train, which will make $7.08 for the six trains, or 
$1.18 per mile for the average of the six trains, rather than 
$1.30 per mile for the five heavier trains. The net differ- 
ence, however, is the 58 c. per mile of road per day. If 
the division to which this applies is 100 miles long, it 
means an added expenditure of $58 per day, or about 
$20,000 per year. 

The student is especially cautioned that the above 
demonstration should be considered as an outhne of a 
method of investigation, rather than a computation of 
values to be used. The separate items should be carefully 
investigated in applying this method to any particular case. 



CHAPTER VIII. 

ECONOMICS OF CAR CONSTRUCTION. 

90. A very large part of the economy which has been 
accomplished in railroad transportation during recent 
years has been due to improvements in the construction 
of freight-cars. In this chapter we must ignore altogether 
the improvements of passenger-cars, since development in 
passenger-car construction has followed the hues of in- 
crease in weight and in the allowable luxury of travel, 
rather than along economical lines. Improvements have 
likewise been made to increase the safety of train opera- 
tions, such as improvements in couplers, air-brakes, etc. 
But the improvements in car construction which have 
tended toward economy in railroad operation have been 
practically confined to freight-cars. These improvements 
consist chiefly in increasing the strength of thecar and its 
capacity, without proportionately increasing its dead- 
weight. This reduction in the ratio of dead load to live 
load has been one of the most potent causes in the reduc- 
tion of freight-charges. But these heavier cars have 
absolutely required improved couplers, which are not 
only more capable of handling the heavier loads but are 
less subject to deterioration and breakage. Another very 
potent means of economy in the handling of freight- trains 
is the application of air-brakes to freight-cars. In fact 
the very heavy trains now operated on some roads could 
not be safely handled, especially at such speeds as are 
used, without the adoption of all these improvements. 

138 



ECONOMICS OF CAR CONSTRUCTION. 139 

91. Weight of cars. — The statistics furnished by the 
Interstate Commerce Commission give a very accurate 
idea of the capacity of the freight-cars used in the United 
States. The total number reported in 1904 was nearly 
1,700,000, with an aggregate capacity of over 50,000,000 
tons. The average capacity is thus about 30 tons, which 
is a very great increase over the corresponding figures of a 
few years ago. The report showed in the hghtest class 
4812 cars with an average capacity of 6 tons, nearly half 
of them being coal-cars. At the heavy end of the hst 
were two cars, each with a capacity of 150,000 pounds. 
About 42% of the total number have the same capacity 
as the average (30 tons), and about 21% have a capacity 
of 40 tons. The increase in the average capacity during 
a single year was about one ton. This statement alone 
is a significant commentary on the economy which has 
been universally demonstrated in the use of cars of large 
capacity. 

92. Ratio of live load to dead load. — A. M. Wellington, 
writing in 1885, gave as the weight and capacity of a 
'^new standard box-car" 24,800 and 50,000 pounds 
respectively. The corresponding figures for the ^'old" 
standard cars were 20,900 and 30,000 respectively. The 
''new standard cars," therefore, had a carrying capacity 
of little over twice their dead-weight, while the carrying 
capacity of the old standard was about 144% of the dead- 
weight. Since then, cars with a carrying capacity of 
60,000, 80,000 and even 100,000 pounds have become not 
only common, but almost standard. As an average figure, 
we may say that the car with a carrying capacity of 
100,000 pounds will weigh about 38,500 pounds. The 
ratio of live load to dead load has been increased from 
144% to 260%. When freight-cars are used to the limit 
of their capacity (at least in the direction of heaviest 
traffic), they are frequently loaded with a five load that 



140 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

is about 10% greater than their rated capacity. It is thus 
seen that the heaviest cars can be, and frequently are, 
loaded with a load which is about 2.86 times the dead 
load. There is, therefore, no exaggeration in the sub- 
sequent calculations on tonnage ratings to consider that a 
train of fully loaded cars has a live load which weighs twice 
the dead load. In fact, such a statement is conservative, 
considering what may be done and sometimes is done. 
93. Economics of high-capacity cars. — The following 
line of argument, showing the economy in heavy cars, is 
condensed from an elaborate presentation of the subject 
by Mr. Rodney Hitt, which was published in the Railroad 
Gazette, May 19, 1905. The advantages are briefly stated 
as follows : 

1. The smaller number of cars which are required to 
transport a given amount of freight. The actual invest- 
ment in equipment is smaller, since the increase in cost is 
not proportionate to the increase in capacity. There is less 
work for the car-service department; the empty car 
movement in the direction of least traffic is decreased. 

2. The number of cars, and even the munber of trains, 
required to handle a given traffic is very materially 
decreased. Economy in this direction might be computed 
in a manner very similar to the computation of the economy 
in using heavier locomotives as given in Chapter VII. 
This economy, of course, involves a saving in the wages 
of train- and engine-crews, an economy which is indepen- 
dent of the number of tons hauied, and which depends 
chiefly on the number of trains required to handle the 
traffic. 

3. There is a saving in the cost of car repairs — per ton 
capacity, if not per car. The amount of this saving is not 
easy to compute, and under some circumstances it is ap- 
parently negative. The high capacity cars are necessarily 
built with steel frames and are sometimes built entirely 



ECONOMICS OF CAR CONSTRUCTION. 141 

of steel. Such cars have estabhshed an enviable record 
by their immunity from material damage during train- 
wrecks, when lighter wooden cars, caught in the same wreck, 
have been utterly destroyed. Although the early designs 
of high-capacity cars were not properly designed with 
respect to draft-gear, wheels, etc., and therefore their records 
of repair charges were abnormally large, improvements 
in design have resulted in a reduction of such charges, 
even below the average figures for the lighter rolling-stock. 
It has been found that the repair charges on lighter 
rolling-stock have been materially increased when such 
cars have been used in the same trains with the heavier 
steel cars, since the effect of a collision or serious bumping 
during careless switching almost invariably results in a 
crushing of the light wooden car, although the heavier 
steel car usually suffers no damage. The cars of latest 
design have shown a very considerable economy in the 
cost of repairs per ton-mile. 

4. There is a reduction in the frictional and atmospheric 
resistance per ton. The frictional resistance per ton de- 
creases with the axle-load. The atmospheric resistance, 
depends almost entirely on the number of the cars. The 
lighter and heavier cars are so nearly of the same size 
that the very shght increase in atmospheric resistance, 
which is due to an increase in size, is of no importance in 
this case. ^'An engine which can haul 1000 tons in 90 
cars can haul 1250 tons in 50 cars at 8 miles per hour, 
and at higher speeds the difference is still greater." 

5. There is a saving in track-room in yards and ter- 
minals. An 80,000-pound car occupies but httle more 
track-room than a 40,000-pound car, while it permits 
twice as much freight to be loaded and unloaded in the 
same time. This consideration is of special importance 
in the congested terminals of the trunk lines at tide-water, 
where land is so very valuable. The recent difficulties of 



142 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

railroads in clearing some of their freight-yards would 
have been very largely augmented if the cars had an aver- 
age capacity of only 10 or 15 tons rather than 30. 

6. There is a saving in switching charges per ton of reve- 
nue load. The cost of moving a car through a division or 
terminal yard varies from 20 to 65 c, as was shown in a 
recent report from one of the large railroad systems. If a 
car is passed through four yards on one trip, the cost of 
switching, etc., may be as high as $2. For a 50-ton car 
this is at the rate of 4 c. per ton, while for a 20-ton car it 
is 10 c. per ton, which is an appreciable difference. 

94. Use of air or train-brakes. — It is needless, in this 
.period of railroad history, to argue the value of air-brakes 
in the operation of trains. According to the report of 
the Interstate Commerce Commission for the year 1904, 
out of nearly 40,000 passenger-cars all but 297 were fitted 
with train-brakes. It is conceivable that even these 297 
are merely old cars, which are wearing out their last years 
of service on lines which are being operated so cheaply 
that even such an improvement is financially impossible. 

Of nearly 1,700,000 freight-cars all but 258,000 (a httle 
over 15%) have been equipped with train-brakes. Even 
this proportion of cars which are not equipped with train- 
brakes is far smaller than it was a few years ago. In 1889 
less than 12% of the total number of cars and locomotives 
were equipped with train-brakes. In fifteen years the 
proportion has been increased from 12 to over 84%. 
It is probably safe to say that no new regular equipment 
is now being built without train-brakes. 

The operation of passenger-trains at high speed, and 
the operation of very heavy freight-trains at almost any 
speed, but especially at high speed, would be absolutely 
unsafe without the use of air-brakes. Their use is now 
so universal and their advantages so well recognized that 
no further comment is necessary. 



ECONOMICS OF CAR CONSTRUCTION. 143 

95. Use of automatic couplers. — The use of automatic 
couplers to replace the old-fashioned link-and-pin coupler 
was ordered by Congress on all cars used in interstate 
traffic. In 1889 the percentage of equipments fitted with 
automatic couplers was less than 8%. In 1904 it had 
increased to nearly 99%. As in the case of the air-brakes 
it is needless to point out the advantages. The old link- 
and-pin coupler was not only inadequate for the heavy 
rolling-stock as used at present, but was always a fruitful 
source of injuries and death to railroad employees, chiefly 
brakemen. With the demand for something to replace 
the old link-and-pin coupler, a multitude of inventors came 
forward with various plans. The Patent Office was be- 
sieged with claims for patents on every conceivable method. 
The interchange of freight-cars among various roads and 
the combinations of such cars into trains imperatively 
demanded that some standard should be adopted, so that 
whatever the details of the coupler all couplers should 
be capable of being used with each other. The Master 
Car-builders' Association therefore adopted a standard 
outline. All the automatic couplers now in use have the 
same essential outline as is shown in Fig. 7. The varia- 
tions of the different designs have to do entirely with the 
details of their method of operation or the manner of their 
fastening to the car-body. 

96. Draft-gear. — The demand for heavier locomotives 
and heavier cars has entailed with it the requirement that 
the draft-gear of cars must be improved. The frictional 
resistance which must be overcome in starting a train, as 
well as the inertia, is very great. But the figures which 
have been determined experimentally as the starting 
resistance are much less than they would be if it were 
not for the slack which always exists to a greater or less 
extent between cars. In the old days of link-couplers, 
especially when the links were fastened to a coupler which 



144 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

was rigidly attached to the car-body without the inter- 
vention of spring draft-gear, although the hnks made 
some slack, the inevitable result was a jerk on the coupler 
which would frequently tear it loose from the car -body, 
even if the car-frame was not badly wrenched or torn 
apart. The adoption of close couplers removed all the 
slack which had formerly existed in the links, and was 
only made practicable by the use of spring draft-gear, 
which permits a yielding either in compression or tension. 
97. Spring draft-gear. — In Fig. 7 is shown an illustra- 
tion of a spring draft-gear and the method of its 
attachment to the car-frame. This is the recommended 
practice as adopted by the Master Car-builders' Asso- 
ciation at their convention in 1896. By vote of the asso- 
ciation it was decided, as their opinion of standard practice, 
that the draft-spring should be GJ'' in diameter, 8'' long, 
and with a permissible motion of 2J''. The capacity of 
the spring was placed at 19,000 pounds. These figures are 
given since they indicate the standard in accordance 
with which a large proportion of the freight-cars now 
in existence were built ; but, as shown later, they are far 
from representing the present standard practice for 
future construction. It should be noted that the essential 
features of such a coupler consist of the yoke A^ which 
passes around the two followers BB which are separated 
by the heavy spiral springs R; the followers BB extend 
out beyond the yoke, where they press against the shoulders 
which are fastened into place by four heavy bolts. During 
compression the front follower presses against the spring 
which transmits the pressure to the rear follower, which, 
in turn, transmits the pressure to the shoulders and the 
car-body. During tension the yoke N is drawn forward, 
which draws forward the rear follower which transmits 
its pressure through the spring to the front follower, 
which, by pressing against these shoulders, draws the car 



ECONOMICS OF CAR CONSTRUCTION. 



145 







Fig, 7. — Spring Coupler, showing method of attachment as recom- 
mended by Master Car Builders' Association in 1890. 



146 THE ECONOMICS OF llAILROAD CONSTRUCTION. 

forward. In either case the spring is compressed. Fig. 7 
also gives in outline form the standard dimensions and 
shape as required for an M.C.B. coupler. No details are 
given, as they are left to the individual designer of the 
coupler. Any couplers which have those same outhne 
dimensions may be operated with any other coupler with 
the same standard dimensions, regardless of their precise 
design. Spring-couplers are used on a very large majority 
of the cars now in service, and they answer their purpose 
as long as the total weight of the cars with their loads is 
not excessive, and provided that the handling of cars in 
freight-yards is done with care. The enormous freight 
business handled by railroads during recent years has 
resulted in a considerable increase in the cost of freight- 
car repairs, which has been due very largely to the fact 
that freight-yard men have been required and urged to 
do their work as quickly as possible. This has resulted in 
a far higher average velocity in freight-yard movements. 
The invariable consequence is a jerking of the cars when 
they are pulled forward and a severe compression of the 
cars when they run together. Considering that the effect 
of impact increases as the square of the velocity, an 
increase in the velocity of yard movement from one mile 
per hour to two or three miles per hour will mean that 
the destructive impact will be from four to nine times as 
great. The adoption of very heavy steel cars has had 
the incidental disadvantage of increasing the cost of 
repairs of the lighter wooden cars, since the heavy cars, 
with their greater weight and especially with the greater 
velocity of freight-yard movement, which is now so 
common, will crush lighter cars between them. The 
inevitable result has been that with the continued growth 
of weight of rolling-stock even the spring principle became 
inadequate. It became necessary to introduce some 
device which would be better capable of absorbing the 



ECONOMICS OF CAR CONSTRUCTION. 147 

very great shocks due to compression and also the jerks 
due to the sudden starting of a very heavy and powerful 
locomotive. This was accomplished by means of ^'fric- 
tion" draft-gear. The committee on draft-rigging of 
the Western Railway Club reported to the club in May, 
1902, on some tests of draft-rigging as follows : 

'Trom the general results of the tests, it is beheved 
that the tensile strains in draft-gears with careful handling 
will frequently reach 50,000 pounds, with ordinary hand- 
ling 80,000 pounds, and with decidedly rough handling 
fully 100,000 pounds, while the buffing strains can be placed 
at 100,000, 150,000, and from 200,000 to 300,000 pounds 
respectively. In extreme cases the buffing strains will 
go considerably above the last-named figure. We think 
the figures show the necessity of something better and 
more effective than the spring draft-gear as commonly used. 
It would be reasonable, in view of the above figures, to 
require draft-gears and underframes to be capable of 
withstanding tensile strains of 150,000 pounds, and 
buffing strains of 500,000 pounds, and it is evident that 
the present spring resistance is inadequate. Whatever 
one may think of the details of the various friction draft- 
gears, it must be evident that in the character and amount 
of resistance they are superior to the spring-gears." 

98. Friction draft-gear. — The principle underlying fric- 
tion draft-gear is that of a device which shall harmlessly 
transform into heat the excessive energy produced by the 
shocks of the operation of trains. The frictional draft- 
gear constructed by the Westinghouse Air-brake will be 
here briefly described. This gear employs springs which 
have sufficient stiffness to act as ordinary spring-couplers 
for the ordinary pushing and pulling of train operations. 
Sections of the gear are shown in Figs. 8 and 9, while the 
method of its application to the framing of a car of the 
pressed steel type is shown in Fig. 10, a and 6. When 



14B THE ECONOMICS OF RAILROAD CONSTRUCTION. 





ECONOMICS OF CAR CONSTRUCTION. 



149 



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150 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

the draft-gear is in tension the coupler, which is rigidly 
attached to B, is drawn to the left, drawing the follower 
Z with it. Compression is then exerted through the gear 
mechanism to the follower A which, being restrained by 
the shoulders RR, against which it presses, causes the 
gear to absorb the compression. The coil-spring C 
forces the eight wedges n against the eight corresponding 
segments E. The great compression of these surfaces 
against the outer shell produces a friction which retards 
the compression of the gear. The total possible movement 
of the gear, as determined by an official test, was 2.42 
inches, when the maximum stress was 180,000 pounds. 
The work done in producing this stress amounted to 18,399 
foot-pounds. Of this total energy 16,666 foot-pounds, 
or over 90%, represents the amount of energy absorbed and 
dissipated as heat by the frictional gear. The remaining 
10% is given back by the recoil. The main release spring 
K is used for returning the segments and friction strips 
to their normal position after the force to close them has 
been removed. It also gives additional capacity to 
the entire mechanism. The auxiliary spring L releases 
the wedge D, while the release pin M releases the pressure 
of the auxiliary spring L against the wedge during frictional 
operation. If we omit from the above design the fric- 
tional features and consider only the two followers A 
and Z, separated by the springs C and K, acting as one 
spring, we have the essential elements of a spring draft- 
gear. In fact this gear acts exactly Hke a spring draft- 
gear for all ordinary service, the frictional device only 
acting during severe tension and compression. 



CHAPTER IX. 



TRACK ECONOMICS. 



In this chapter will be discussed some of the items of 
the cost of track construction and maintenance, which are 
so large and important that they should be studied with 
great care, in order to discover any possible economies. 
Chief among these items are the costs of rails and ties. 
A very brief study of the subject will show that variations 
in the weight and character of the rolling-stock, the rate 
of grade, the amount and sharpness of curvature, etc., 
will modify the expenditure which may, with the best 
economy, be made on these two items. 

Rails. 

99. Rail wear — theoretical. — Definite information on 
this subject is very difficult to obtain. If rails were only 
renewed when a certain proportion of their total weight 
had been worn away — say one-quarter of the head or 
about 10% of the total weight — then it would be a com- 
paratively simple matter to estimate the effect of aline- 
ment on rail wear. But it frequently, if not generally, 
happens that rails on tangents are removed, not on account 
of wear on the head, but on account of failure at the joints. 

When the steel of a rail is comparatively soft and duc- 
tile, the effect of concentrated wheel-pressure is to cause 
an actual flow of the metal, so that it will spread outside 
of its original outline, as is shown in the figure. The burr 

151 



152 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

on the inside of the head will generally be worn off by the 
occasional pressure of a wheel-flange against the rail. The 
top of the rail will be w^orn with a slight slope to the inside, 
which corresponds somewhat with the coning of the wheels. 
Fig. 11 shows the usual outline of a worn rail on the 
outside of curves. The wear is largely on the inner side 
of the head, the side of the head being practically gone 
before the top of the rail is much worn. The inside rail 
of a curve will wear to about the same form as a rail on 
a tangent, as shown in Fig. 12, but the wear is much faster. 









Fig. 11. 



Fig. 12. 



Fig. 13. 



Rail wear on curves is due chiefly to two causes: slip- 
ping due to unequal length of the rails and grinding of the 
side of the head by the wheel-flanges. 

(a) Longitudinal slipping. When a pair of wheels 
which are not rigidly attached to their axle run around 
a curve (see Fig. 13), the outer wheel must roll a distance 

-^^r2 and the inner wheel will roll a distance of 

, 2;ra° , 2-«° 

The difference equals -^gQ5(r2-ri) or -^^ 

that when the wheels are fixed for any one gauge (g), the 
slipping is proportional to the number of degrees of central 
angle, equals ca°, and is independent of the radius. This 
slipping must be accomplished by the inner wheel slip- 
ping forward or the outer wheel slipping backward, or by 
a combination of the two which will give the same total 
amount of slipping. It is quite probable that the most of 



360°^'* 
This shows 



TRACK ECONOMICS. 



153 



the slipping occurs on the inner rail, and that this accounts 
for the great excess of rail wear on the inner rail of a 
curve over that on a tangent. 

(b) Lateral slipping. The two (or three) axles of car- 
trucks and the two or more driving-axles of a locomotive 
are always set exactly parallel to each other. This is done 
so that each pair of wheels shall mutually guide the other 
and maintain each axle approximately perpendicular to 
the rails. If the two axles of a truck are not exactly 
parallel, the truck has a constant tendency to run to one 
side, producing additional track resistance, rail wear, and 
wheel-flange wear. When two pairs of wheels with parallel 
axles are on a curve, the planes of at least one pair of 
wheels must make an angle with the tangent to the rails. 
When the radius of the curve is very short compared with 
the length of the wheel-base (as generally occurs at the 
street-corners of street-railways), then both axles will 
make angles with the normals to the curve, as shown in 
Fig. 14. The normal case for ordinary railroad work 
with easy curvature is that shown in Fig. 15, in which 
the rear axle stands nearly or quite normal to the curve, 
while the front axle makes an angle 0° with the normal, 




Fig. 14 



Fig. 16. 



and the plane of the wheel makes an angle of a° with the 
rail. The relative position of the outer front wheel and 
the rail is shown more clearly, although in an exaggerated 
way, in Fig. 16. The wheel tends to roll from a to h. 
Therefore, in moving along the track from a to c, it rolls 



154 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

the distance ab and slides laterally the distance he, which 
equals ac sin a. In the usual case (Fig. 15) sin a = t-^r. 
When t = 5' and r = 5730', the radius of a 1° curve, a = 0° 03'. 
For the usual radii of railroad curves a will vary almost 
exactly with the degree of the curve. For example, on a 
6° curve, using a 5-foot wheel-base, a = 0°18' and sin a 
= .0052. For each 100 feet traveled along a 6° curve, 
the lateral slip of the front wheels is 0.52 foot, or about 
GJ inches. If the rear axle remains radial there is no lat- 
eral slipping of the rear wheels. 

It can readily be seen that when the angle a is large, 
the wheel-flange continually grinds the side of the head 
of the rail. The larger the angle the more direct and 
destructive is the grinding action. 

100. Rail wear — statistics. — It is very difficult to ob- 
tain reliable figures regarding rail wear and especially of 
the rail wear on curves. Such figures as are obtainable 
are almost hopelessly contradictory. The author has 
corresponded with the Chief Engineers or Engineers of 
Maintenance of Way of several prominent railroads in 
the hope of collecting such data. Very few satisfactory 
answers were obtainable. Usually the answers gave 
merely the average total life of rails on tangents and 
on various curves. It should not be forgotten that 
almost the only value of the figures quoted below lies in 
the statement of the relative life on the various curves 
of any one division of a road where the rails are of the 
same kind and are subject to exactly the same train-loads. 
One such statement is given by Mr. W. B. Storey, Jr., 
Chief Engr. of the A. T. & S. F. Rwy. The statement 
gives the approximate times of rail removal of 75-lb. 
A. S. C. E. rails on mountain curves of that road, on 
which the freight-trains are hauled by " Santa Fe " 
engines, which are decapods with trailing wheels, and have 
a very long wheel-base. 



TRACK ECONOMICS. 



155 



Table XIII. — Life (in Months) op Rails on Mountain Curves- 
A. T. & S. F. RwY. 





10° 


8° 


6° 


5° 


40 


3° 


Outer rail 

Imier rail 


9 mo. 
18 mo. 


15 

24 


24 

48 


40 
60 


56 

72 


/6to8 

I yrs. 







The relative life of these rails is better appreciated by a 
consideration of the curves of Fig. 17, 



IBO 



100 



80 



40 























\ 




















\ 




















\ 




\ 

\ 
















\ 


V 


^x, 


















\ 


>^ 


\ 
















\ 


s 


\ 


\ 
















>'\ 


\ 
C 




















^ 




% 


^\r- 














k 


\ 






\ 














% 






\ 


^^ 


















^ 


^^>^ 

























a JL° 2° 3° 4° 5° 6' 7° 8° 9° iO 

Degree of curve. 

Fig, 17. — Total rail life in months. 

A similar statement was furnished by Mr. A. C. Shand, 
Chief Engr. of the P. R.R. This statement does not 
differentiate between the wear on the outer and inner 
rails. It gives the average life of 100 rails which are sub- 
ject to the very heavy traffic of their main Hne. 



156 THE ECONOMICS OF RAILROAD CONSTRUCTION, 



Table XIV. — Life (in Months) of 100-lb. Rails — Main Line, 

P. R.R. 



Tangent 


1° 


2° 


40 


6° 


8° 


9° 


120 mo. 


96 


60 


30 


20 


14 


9 



The curve indicating these values has also been shown 
in Fig. 17. 

A comparison of these rates of wear apparently indicates 
that, although the rate of rail wear is less (under the given 
conditions) on the A. T. & S. F. than on the P. R.R., the 
reduction in rail life^ by increasing the curvature from 4° 
.to 9°, is far greater on the A. T. & S. F. than on the P. R.R. 
More important, however, is the agreement of both curves 
that they are concave upward. A considerable part of 
rail wear is independent of whether the track is curved 
or straight. The rails on a curved track are subject to 
all forms of wear which reduce the life of rails on a straight 
track and much other wear in addition. If we draw a 
straight horizontal line through the '^120," the vertical 
distance down to the P. R.R. curve at any point indicates 
the reduction in the life of the rail on account of curvature. 
This reduction is less per degree of curve as the curvature 
is sharper. Although we do not know where the ^^ tangent" 
ordinate belongs for the A. T. & S. F. curves, it is evident 
that the same principle holds good. This only verifies 
the theoretical deduction previously made that the 
longitudinal slipping (and the amount of rail wear it ' 
causes) is independent of the radius. 

10 1. Rail-wear statistics on the Northern Pacific R.R. — 
Some five-year tests have just been made on the Northern 
Pacific Railroad to determine the actual wear of rails 
under a measured amount of traflBc. Apparently one 
object of the investigation was to determine the effect 
of variation in the chemical composition of the rails. A 



TRACK ECONOMICS. 



157 



pair of each of five types of rails were tested in each of 
eight situations ; six of them being on the Pacific division 
and two on the Minnesota division. No attempt will 
be made here to analyze the effect of variation of chemical 
composition, but, since one of each kind of rail was used 
in each locality, the average of all rails for each locality 
will be considered as the typical rail for such an aline- 
ment and grade. The rails were actually weighed each 
year for five years, so that their actual loss in weight 
during each year's wear could be determined. The 
tonnage passing over these rails was systematically 
recorded. It varied for these eight localities between 
27,021,227 and 29,862,738 tons. For uniformity in each 
case, the wear was reduced to the uniform basis of 
10,000,000 tons. Even though the wear is not strictly 
proportional to the tonnage, the variation between 
27,021,227 and 29,862,738 is not large enough to cause 
any serious error from this source. The wear of the 
rails on the tangents in per cent per 10,000,000 tons' 
duty is given in the following tabular form. 

Table XV. — Rail Wear on Tangents, Northern Pacific R.R. 



Five pairs of rails on first 

tangent, Pacific div= ; 

grade, 0.3%. 


Five pairs of rails on second 

tangent. Pacific div. ; 

grade, 0.525%. 


Five pairs of rails on third 
tangent, Minnesota div, ; 
grade chiefly level at bot- 
tom of sag. 


Pet. loss 
in four 
years. 


Pet. loss per 
10,000,000 . 
tons' duty. 


Pet. loss in 
four years. 


Pet. loss per 
10,000,000 
tons' duty. 


Pet. loss in 
four years= 


Pet. loss per 
10,000,000 
tons' duty. 


1.800 
2.336 
1.806 
2.015 
1.706 


.603 
.783 
.605 
.676 
.572 


.960 
.900 

1.360 
1.256 
1.807 


.346 
.324 
.490 
.452 
.391 


.451 

.825 

1.135 

.822 
.280 


.167 
.305 
.420 
.304 
.104 




.648 




.401 




.260 



It may be at once noticed that the average loss in per 
cent per 10,000,000 tons' duty on the first tangent was 



158 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

9.648%; on the second tangent it was only 0.401%. In 
the endeavor to discover the cause of the uniformlv 
increased wear of the rails on the first tangent over that 
on the second tangent, the grade of the two tangents 
was considered, but the grade of the first tangent was 0.3%, 
while that of the second tangent was 0.525%. As rail 
wear is usually greater on steep grades than on flat grades, 
owing to the slipping of the driving-wheels when climbing 
the grades, or the possible skidding of the wheels when 
moving down the grade with brakes set, the results are 
here relatively contrary to what we would expect. The only 
apparent explanation of the increased rail wear on the 0.3% 
grade is that it occurs near the bottom of a very long down 
grade, where a train might have acquired a high velocity 
and where the wheels might have skidded in the attempt 
to hold the train, or where engines, hauling a train up grade, 
are doing their utmost (perhaps by using sand) to obtain a 
sufficiently high velocity to carry their trains by momen- 
tum over the long grade. In the case of the 0.525% grade 
this tangent occurs at the very upper end of the grade, 
where the velocity in either direction is probably lower 
than the average. Whether this is the true explanation, 
the relative wear on these two tangents for all makes of 
rails is uniformly as stated above. 

102. Relation of rate of rail wear to the life-history of 
the rail. — The figures obtained during the above-described 
tests of rails on the Northern Pacific Railroad afford some 
very instructive and apparently reliable data regarding 
the rate of rail wear in its relation to the life-history of 
the rail. The rails were taken up and weighed each year 
for a period of four or five years; the loss of weight in 
pounds for each yearly interval then becomes known. 
It is usually stated that rail wear is comparatively small 
during the first half of the life of the rail and that the 
rate of wear grows in geometric ratio. It is usually sup- 



TRACK ECONOMICS. 



159 



posed that this is more especially true of rails on sharp 
curves than on easy curves or on tangents. A study of 
the tabular values given in the report are interesting in 
this respect, for the figures seem to contradict this theory. 
The annual losses on the outer rails of 10° and 10° 30' 
curves were as follows : 



10° curve; grade, 
0.128% 



Table XVI. — Yearly Wear (in Pounds) of Outer Rails — Sharp 

Curves. 



5th Year, 

21.0 
13.5 
21.25 
11.25 

15.75 

16.55 

19.25 
6.25 

15.0 
2.5 
6.25 

9.85 



Average. 



10° 30' curve; grade, 
0.3% 



Average. 



1st Year. 


2d Year. 


3d Year. 


4th Year. 


13.75 

11.75 

13.25 

5.75 

9.75 


13.75 
9.75 
9.75 
7.25 
7.25 


11.75 
9.75 
9.75 
1.75 
5.75 


18.25 

12.0 

16.5 

4.5 

7.0 


10.85 


9.55 


7.75 


11.65 


13.75 

13.5 

10.75 

12.0 

12.25 


7.75 
5.25 
7.75 
4.25 
4.75 


10.25 
9.25 

15.25 
4.75 
9.75 


5.5 
19.25 
15.0 
15.0 

7.5 


12.45 


5.95 


9.85 


12.45 



Similar figures for the wear of rails on tangents are 
given in Table XVII. 

So many rails are involved in the above tests that we can 
hardly ignore the indications given by the averages espe- 
cially when the different lines of averages seem to vary 
by an approximately similar law. Apparently rail wear 
during the first year is greater than during the second and 
third years; during the fourth year it increases to about 
the same as during the first year, while the wear during 
the fifth year is usually far greater. If we ignore the 
three abnormally low values given for the fifth year on 
10° 30' curves, the average of the other seven values is 
16.71 pounds per year, which is an increase over the fourth 



160 THE ECONOMICS OF RAILROAD CONSTRUCTION. 
Table XVII. — Yearly Wear (in Pounds) of Rails on Tangents. 



Grade. 

0.3% { 

0.525%... I 

0.3% I 

0.525% 

0.3%. 

0.525% { 

0.3% 

0.525%, 

0.3% 

0.525% I 

Average, . 3% 

0.525% .. . 

General average 



1st Year. 



3.0 
3.25 
2.5 
0.25 



50 
75 


25 

75 

50 

75 

75 

25 

25 

3.25 

2.75 

2.75 

4.25 

2.5 

1.0 



3.82 
2.10 



2.96 



2d Year. 



3.0 

3.25 

4.25 

3.25 

4.25 

4.75 



25 

75 

,25 

25 

75 

,75 

2.75 

0.25 

1.75 

3.25 

2.75 

2.75 

3.25 

1.75 



2.82 
2.90 



2.86 



3d Year. 



3.0 
2.75 

0.75 

0.50 

2.25 

2.25 

0.25 

0.0 

0.75 

4.75 

0.75 

0.25 

1.5 

4.25 

0.75 

0.25 

2.75 

3.75 

0.5 

2.75 



2.80 
0.67 



1.74 



4th Year. 5th Year, 



3.25 

2.25 

1.50 

4.75 

6.50 

4.25 

0.50 

0.75 

2.50 

4.50 

1.0 

0.50 

3.25 

5.75 

2.75 

3.25 

3.5 

2.25 

0.25 

3.5 



3.80 

1.87 



2.84 



6.0 
2.25 
9.0 
7.0 
2.25 
6.25 
8.50 

10.25 
1.25 
2.25 
2.25 
2.0 
3.25 
1.75 
5.75 

14.0 
6.25 
7.5 
4.75 
6.25 



3.90 
6.97 



5.94 



year such as we might expect. It may be noticed in 
passing that all of the rails on the 10° curves were noted 
as being "badly worn" and that the rails on the 10° 30' 
curves were actually replaced. The rails on the 10° 30' 
curve averaged 648 pounds in weight and they had lost an 
average of nearly 50 pounds, or about 8%, before being 
replaced. The rails on the 10° curve averaged 679 pounds 
in weight and they had lost a little over 56 pounds apiece, 
which was little over 8% on their weight. They had not 
been actually renewed, although they were indicated as 
''badly worn." 

103. Rail wear on curves.— In Table XVII is given an 
analysis of the figures furnished for the rail wear on 
various curves of the Pacific division of the Northern 



TRACK ECONOMICS. 



161 



Pacific Railroad. The method adopted was to determine 
the percentage loss in four years. This percentage was 
divided by the tonnage (varying between 27,021,227 and 
29,862,738 tons) to reduce it to the uniform basis of the 
wear for 10,000,000 tons' duty. By dividing the quantities 
in column 3 by the average percentage loss (0.525%) 
on two tangents subject to the same traffic, of this same 
division, we have the ratio of the rail wear on a curve 
to the rail wear on the average tangent. Subtracting one 
from each one of the quantities in column 4 we have 



Table XVIII. 



-Rail Wear on Curves- 
Pac. Div. 



-Northern Pacific R.R., 



Degree of 
curve. 



4° 31'. 



5°0'. 



10° 0' . 



10° 30' 



Pet. loss 
in four 


Pet. loss 
10,000,000 


Col. 3 
H-.525. 


Excess 


Excess 
per 


years. 


tons' duty. 




degree. 


2.675 


0.964 


1.838 


0.838 


.185 


2.970 


1.070 


2.038 


1.038 


.230 


2.912 


1.049 


1.999 


0.999 


.221 


1.781 


0.642 


1.223 


0.223 


.049 


1.877 


0.676 


1.238 


0.288 


.064 


3.500 


1.173 


2.235 


1 . 235 


.247 


3.271 


1.096 


2.087 


1.087 


.217 


4.349 


1.450 


2.761 


1.761 


.352 


2.857 


0.957 


1.823 


0.823 


.165 


4.450 


1.491 


2.840 


1.840 


.368 


5.150 


1.855 


3.534 


2.534 


.253 


4.417 


1.590 


3.030 


2.030 


.203 


6.205 


2.238 


4.265 


3.265 


.326 


2. 087 


0.751 


1.430 


0.430 


.043 


3.122 


1.124 


2.141 


1.141 


.114 


6.200 


2.080 


3.9G0 


2.960 


.282 


6.022 


2.020 


3.850 


2 . 850 


.272 


5.610 


1.882 


3.588 


2.588 


.247 


3.704 


1.241 


2.365 


1.365 


.130 


3.795 


1.272 


2 . 423 


1.423 


.136 



Average 

excess per 

degree. 



150 



.270 



.188 



:i3 



the excess w^ear, which may be considered due to curva- 
ture alone. By dividing these quantities in column 5 by 
the degree of the curve we have the excess per degree. 



162 THE ECONOMICS OF RAILROAD CONSTRUCTION. 



The average of the five values in each case is given in 

column 7. The significance of these numbers in column 

7 may be interpreted as follows: .150, for example, 

means that the excess wear per degree of curve on the 

150 
various rails of the 4° 31' curve averaged -jk?^ of the wear 

on an average tangent. The other figures in the last 
column are to be interpreted similarly. The 4° 31' curve 
was on a 0.525% grade, the 5° curve was on a 0.3% grade, 
the 10° curve was on a 0.128% grade, and the 10° 30' 
curve was on a 0.3% grade. The rate of grade on these 
curves evidently does not account for the variations in 
these values. It is quite apparent that the rail wear per de- 
gree of curve for the sharper curves does not increase with 
the curvature, and it is more than likely that it dimin- 
ishes, as was indicated by the diagrams given in § 100. 
A similar computation was made from the results of 
the wear on a 3° curve on the Minnesota division. See 
Table XIX. 

Table XIX. — Rail Wear on Curves — Northern Pacific Railroad 
Minnesota Division. 



Degree of 
curve. 


Pet. loss 
in four 
years. 


Pet. loss 
10,000,000 

tons' duty. 


Col. 3 
-^ .280. 


Excess 
over one. 


Excess 

per 
degree. 


Average 

excess per 

degree. 


3° 0' 


1.208 
1.030 
1.538 
1.314 
1.6j7 


.447 
.392 
.569 

.487 
.613 


1.718 

1.507 

2.188 
1.872 
2.358 


0.718 

0.507 

1.188 
0.872 
1.358 


.239 
.169 

.396 
.291 
.453 


1 
.310 



Here the average excess per degree amounted to 31% 
of the rail wear on the tangent. The average percentage 
of excess per degree on the curves of the Pacific division 
was 20.5%; for the one curve on the Minnesota division 
it was 31%; allowing the average for the four curves a 
weight of four and giving a weight of one for the curve 



TRACK ECONOMICS. 163 

on the Minnesota division, the weighted mean is 32.6%. 
Anticipating a demand in a future chapter (Chapter XIII) 
for the effect of curvature on the cost of the renewal of 
the rails, we might state, as an approximate average 
figure, that, since the excess rail wear per degree of curve 
does not seem to increase with the curvature, it is a safe 
conclusion to say that it varies with the degree or curva- 
ture, and that therefore the excess rail wear on a 10° curve 
will be 326% of the rail wear on a tangent. 

Economics of Ties. 

104. Importance of the subject. — The cost of rails is 
frequently the largest single item in the cost of constructing 
a railroad, the cost of the ties usually being less than one- 
half the cost of the rails. This familiar fact is apt to 
cause the engineer to lose sight of the fact that the relative 
cost for maintenance is reversed. For the last ten years 
the average cost of maintaining ties on the railroads of 
the country has been a httle over twice the cost of main- 
taining the rails. The amount actually spent in 1904 was 
nearly $34,000,000, or nearly 3% of the total operating 
expenses. The enormous number of ties annually con- 
sumed in track maintenance is so depleting the forests of 
the country that the price of timber has advanced very 
greatly during the last few years, and it has become a 
question of national importance which is engaging the 
attention of the United States Government. Therefore 
any method which will increase the life of a wooden tie 
is a matter of great importance, not only to the railroads 
but also to the community in general, since the whole 
lumber industry has been very largely affected by the 
use of timber for railroad- ties. 

105. Methods of deterioration and failure of ties. — The 
failure of ties is due to some one or to a combination of 
a large number of causes. First, the wood may decay. 



164 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

Second, the wood may be so soft that the holding power 
of the spikes may be small and this requires that the spikes 
must be frequently re-driven in order to hold the rails. 
Since th'^ tie must be placed symmetrically under the rails, 
the available area for driving spikes is very limited, and it 
sometimes happens that an otherwise sound tie must be 
taken out because it has been '^ spike-killed." Third, 
the tie may be so soft that it is crushed by the concen- 
trated pressure of the rail-flange and especially by the 
pressure of the outer flange of the outer rail on curves. 
This form of destruction is largely obviated by the com- 
paratively inexpensive device of tie-plates. 

io6. The actual cost of a tie. — The actual cost of 
a tie equals the total of several items, of which the 
first cost is but one item. It must be transported 
from the place of sale and delivery to the road to the 
place where it is to be used. A certain amount of, 
track-labor is necessary to place the tie in the track. 
A considerable amount of track-labor is necessary to 
maintain the track at a proper surface. The amount of 
this labor will depend considerably on the length, width 
and weight of the tie, since a large heavy tie has such a 
hold in the ballast that it is not so easily disturbed by 
the passage of trains. Since the cost of track-labor is such 
a very important item in the total cost of a tie, a tie which 
can be kept in the track for a greater length of time and 
with less work for maintenance may be far more econom- 
ical in the long run than a tie which has cost less 
money. The annual cost of a system of ties may be 
considered as the sum of (a) the interest on the first cost, 
(h) the annual sinking-fund that would buy a new tie 
at the end of its life, and (c) the average annual cost of 
maintenance for the life of the tie which includes the 
cost of laying and the considerable amount of subsequent 
tamping that must be done until the tie is fairly settled 



TRACK ECONOMICS. 



165 



in the road-bed. The following very conservative estimate 
of the relative cost of untreated ties and ties which have 
been treated chemically is given as follows: the cost of 
the untreated tie is estimated at 40 c, while the cost of 
the chemical treatment is assumed to be 25 c, making 
the total cost of the treated tie 65 c. The life of the 
untreated tie is assumed to be seven years and that of 
the treated tie fourteen years. The annual interest on 



the first cost estimated at 



will therefore be 1.6 and 



2.6 c. respectively. The sinking-fund at 4% which would 
renew each tie at the given cost at the end of its estimated 
life will be 5.1 and 3.6 c. respectively. The average an- 
nual cost of maintenance is very difficult to estimate, but, 
since we are seeking a comparison rather than a definite 
estimate of cost, all that we need to know is the excess 
of the cost of one method of construction over the other. 
Owing to the impracticability of giving a definite figure 
for item (c) we will assume that it balances for the two 
methods, but with the understanding that the advantage 
is very distinctly with the treated tie and that the advan- 
tage extends not only to the comparative cost of track- 
work but also the indefinite saving in operating expenses, 
due to less jar of the rolHng-stock on a smoother track, less 
cost of repairs, less consumption of energy by the locomo- 
tive, and all the advantages of a smoother track. Collect- 
ing these items we have the tabulated form as follows: 





Untreated 
tie. 


Treated 
tie. 


Original cost. .... 


40 cents 
7 years 


65 cents 


Life (assumed at) 


14 years 




Item (a) — interest on first cost at 4% 

' ' (b) — sinking-fund at 4% 


1 . 6 cents 
5.1 " 


2 . 6 cents 
3.6 " 


" (c)— (considered here as balanced) 




Average annual cost (except item (c)) 


6 . 7 cents 


6 . 2 cents 



166 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

107. Chemical treatment of ties. — The methods of 
chemical treatment of ties will not be here discussed, as 
it may be found in numerous text-books. It is not easy 
to obtain an accurate estimate of the effect of chemical 
treatment, unless reliable figures showing the total life 
in the track of a very large number of ties are obtainable. 
It frequently happens that, owing to some imperfection 
in the tie or some error in its treatment, a treated tie 
may not last even as long as a wooden untreated tie. It 
is only by obtaining the average figures for a very large 
number of ties (at least several thousand) that a true 
measure of the economy of chemical treatment can be 
obtained. The lack of accurate figures is due largely to 
the fact that it is practically a difficult matter to keep 
track of the actual life of the ties. Chalk-marks, and even 
numbers stamped with dies, are easily obliterated in a 
few years. Marking the ties with tacks arranged to form 
letters seems to be the best method, and it has therefore 
been largely adopted by railroads w^hich have determinedly 
made a study of this question. But such a method 
involves trouble and work which few roads have been 
willing to make. Even when figures have been obtained 
regarding the life of ties, it will be found that, of a lot of 
ties which are supposed to be uniform and whose average 
life is supposed to be say seven years, a considerable 
percentage of the ties may need to be removed in two or 
three years, while a very considerable percentage of them 
may still be in the track after 12 or 15 years' service. 
Similar figures are found for the life of chemically treated 
ties, some of them requiring removal after a very few 
years' service, while others will last much longer than 
could be claimed by the promoters of that particular sys- 
tem of tie treatment. It therefore becomes necessary in 
comparing the life of untreated ties with treated ties, or 
in comparing the life of ties treated with different methods 



TRACK ECONOMICS. 167 

of treatment, to compare the percentages of removals 
after a given period of years. It practically amounts to 
the same thing to determine for each kind of tie or 
each method of treatment a curve, showing the number 
of ties as one set of ordinates, and their corresponding 
life for the other. The comparison of such curves 
will show which manner of treatment gives the best 
results. 

io8. Comparative value of cross-ties of different mate- 
rials. — Through the courtesy of Mr. W. C. Gushing, Chief 
Engineer of Maintenance of Way, Pennsylvania Lines West 
of Pittsburg, S. W. System, the author is enabled to quote 
very largely from a paper published by him in Bulletin 
No. 75 of the American Railway Engineering and Main- 
tenance of Way Association. Mr. Gushing made an 
investigation, with a view to determining, as closely as 
possible, the relative value of concrete and steel cross-ties, 
taking cost and prospective Hfe into account, as com- 
pared with the wooden cross-ties at present in use. The 
author states that ^^some of the data used are costs estab- 
lished from actual practice and from reliable information 
given, while in other cases assumptions have been made 
after examining the most reliable information available. 
It is quite true, of course, that these figures cannot be 
considered as absolutely correct, but it is believed by the 
writer that they are fairly trustworthy." The author 
develops his values on the basis of the formula proposed 
by Mr. S. Whinery, in the '' Railroad Gazette " for November 
11, 1904. In order to eliminate any difference due to 
variability of tie-spacing, all results have been reduced to 
the cost per linear foot of track. 

This annual cost per linear foot of track may be ex- 
pressed algebraically thus : 

Let X = the required annual cost of ties per linear foot 
of track; 



16S THE ECONOMICS OF RAILROAD CONSTRUCTION. 

c = the first cost in the track per linear foot of 

track; 
i' = the value of the worn-out tie per linear foot 

of track; 
L = the useful life of the tie in years. 
i = the rate of interest = the interest on $1.00 for 

one year; 
s = an annual payment into a sinking-fund which 
at i rate of interest for L years will amount 
to one dollar (s can be taken directly from 
tables such as that on page 16 of Kent's 
Mechanical Engineers' Pocket-book) : 
Then x = ci + {c — v)s. 

If v = 0, then x = c(i + s). 

On the basis of the above formula, Mr. Gushing made 
three tabulations which have not been copied. Table I 
shows the ^'cost delivered which a .white-oak tie lasting 
10 years must reach before it will be economical to use 
any of the ties heading the columns." The ties considered 
in this table were made of white oak untreated, inferior 
woods treated with zinc-chloride and zinc-tannin, but 
using no tie-plates, also ties of inferior woods using tie- 
plates and treated with zinc-chloride, zinc-tannin, zinc- 
creosote, and with creosote costing 30 and 85 cents 
per tie, also steel ties costing $1.75 and $2.50; also con- 
crete ties costing $1.50 and $2.25. Table II shows ^'how 
long ties of different materials must last in order to be as 
economical as white oak costing 70 cents and lasting ten 
years." Table III shows ^' first cost which can be paid for 
different kinds of ties in order to be as economical as white 
oak costing 70 cents and lasting ten years." The kinds of 
tie considered and also their chemical treatment, if any, 
are the same in Tables II and III as were stated for Table 
1. From these various tables Mr. Gushing made the fol- 
lowing deductions. 



TRACK ECONOMICS. 1^9 

DEDUCTIONS FROM TABLE I. 

(1) With white-oak ties costing 70 cents dehvered on 
the raihoad, it is economical at the present time to buy 
inferior woods at a price not to exceed 50 cents, have them 
treated with zinc-chloride or zinc-tannin, lay them in the 
tracks without the use of tie-plates (except where it is 
necessary to use them on oak ties), and use a standard 
railroad spike. A life of ten (10) or eleven (11) years has 
been found to be a maximum for such ties without the use 
of tie-plates and better fastenings, and if the hfe of ten (10) 
years is not attained, there will be that much loss to the 
company. 

(2) When a white-oak tie reaches a cost of 86 or 
87 cents dehvered on the railroad, it will be economical 
to use the zinc-creosote process, or straight creosote cost- 
ing 30 cents, if the tie costs 46 cents delivered on the rail- 
road and will last (16) sixteen years; or it will be econom- 
ical to use straight creosoting costing 85 cents for treat- 
ment if the tie can be made to last thirty (30) years, 
which is French practice, before the oak tie reaches a cost 
of 80 cents delivered on the railroad. In both of these 
cases it is assumed that tie-plates, wood screws, and heli- 
cal linings are used because ties cannot be made to last 
more than ten (10) or twelve (12) years without the use 
of proper fastenings, since, otherwise, the tie will be de- 
stroyed by mechanical wear. It is necessary, therefore, 
to use improved fastenings when we expect to obtain a 
life of ties greater than ten (10) or eleven (11) years. 

It will also be economical to use a steel tie costing $1.75 
delivered if it will last twenty (20) years. 

(3) When the white-oak tie reaches a cost of 90 cents 
delivered on the railroad, it will be economical to use 
either ties of inferior woods treated with zinc-tannin if a 
life of fourteen (14) years can be obtained, the improved 



170 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

fastenings being used, or a concrete tie costing $1.50 if 
it will last twenty (20) years. 

(4) When the price of white-oak ties reaches $1, it 
will be economical to use a steel tie costing $2.50 if it will 
last thirty (30) years, a concrete tie costing $2.25 if it 
will last thirty (30) years, or an inferior wood tie treated 
with zinc-chloride if a life of twelve (12) years can be 
obtained. 

DEDUCTIONS FROM TABLE II. 

(5) With ties of inferior woods costing 46 cents deliv- 
ered on the railroad we must obtain a life of from eighteen 
(18) to twenty (20) years, whether treated with zinc- 
chloride, zinc-tannin, or zinc-creosote, to make them as 
economical as white-oak ties costing 70 cents. It is 
assumed, of course, that they must have the most ap- 
proved fastenings in order to attain an age as great as that. 

(6) With inferior woods costing 46 cents delivered on 
the railroad, and if the creosoting costs 30 cents, it will 
be necessary for us to obtain a life of twenty-one (21) 
years in order to make them as economical as white-oak 
ties costing 70 cents dehvered. 

(7) With inferior wood ties costing 46 cents dehvered, 
and with the creosote treatment costing 85 cents, as in 
French practice, it will be necessary for us to obtain a 
Ufe of thirty-six (36) years from the ties in order to make 
them as economical as white-oak ties costing 70 cents 
delivered. 

(8") With steel ties costing $1.75 each delivered, it will 
be necessary for us to obtain a life of twenty-eight and 
one-half (28^) years in order to have them as economical 
as white-oak ties costing 70 cents delivered. This price 
is a little less than the cost of the Buehrer steel ties in the 
tracks at Emsworth. 



TRACK ECONOMICS. 171 

(9) With concrete ties costing $1.50 each dehvered, it 
will be necessary for them to last twenty-eight (28) years 
before they will be as economical as the white-oak ties 
costing 70 cents delivered. 

(10) With steel ties costing $2.50 delivered and concrete 
ties costing $2.25 delivered, which are approximately the 
prices of the Seitz steel tie and the Buehrer concrete tie 
in the tracks at Emsworth, it is necessary for them to last 
over fifty (50) years each in order to make them as eco- 
nomical as the white-oak ties costing 70 cents delivered. 

DEDUCTIONS FROM TABLE III. 

(11) In order to make treated inferior woods as economi- 
cal as white oak costing 70 cents delivered, when the 
treated ties are equipped with proper fastenings in order 
to make them last as long as has been found practicable 
by experience, we can only afford to pay for the ties deliv- 
ered on the railroad, 10 cents each when treated with zinc- 
chloride; 20 cents each when treated with zinc-tannin 
or creosoted at 30 cents; 23 cents each when treated with 
zinc-creosote, and 29 cents each when creosoted in accord- 
ance with French practice. 

(12) In order to make them as economical as white-oak 
ties costing 70 cents delivered, we can only afford to pay 
$1.48 each for steel ties which last twenty (20) years, and 
$1.79 each when lasting thirty (30) years. 

(13) In order to make them as economical as white-oak 
ties costing 70 cents dehvered, we can only afford to pay, 
as first cost of concrete ties delivered, $1.15 each if they 
last twenty (20) years, and $1.57 each if they last thirty 
(30) years. 

(14) We know nothing about the life of concrete ties, 
and it is at least very desirable to experiment with them 
for yard and side tracks, even though we do not use them 
in the main tracks, because they might he undisturbed in 



172 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

yard tracks for many more years than they would in 
main tracks. 

(15) When white-oak ties are costing 70 cents dehvered 
(about present prices), we can afford to buy inferior oak 
and other hard woods at 45 to 50 cents (present prices) 
and have them treated with the zinc-tannin or zinc-chloride 
processes, and only use common spike fastenings. 

109. Economy due to form of tie. — The standard practice 
in this country, especially in parts of it where rigid economy 
in the use of ties is not essential, is to use a tie with a 
rectangular cross-section. An attempt at economy has 
been made by adopting a form of tie which would permit 
a greater number of ties to be sawed from the same tree 
trunk. The Great Northern Railroad has been experi- 
menting with triangular ties, cut by sawing the maximum 




Fig. 18. — Method of cutting 
four triangular ties from 
one tree. 



-Hj 

Fig. 19.— Method of cutting 
two triangular ties from 
one tree. 



square obtained from a tree trunk into four parts by 
cutting through the diagonals. In this way four trian- 
gular ties would be obtained from a tree trunk, as shown 



TRACK ECONOMICS. 



173 




in Fig. 18, from which only two rectangular ties could be 
obtained. If the tree trunk is so small that the cross- 
sections of the ties would be too small when cut in this 
form, then two triangular ties would be cut from the trunk, 
as shown in Fig. 19. When tie-plates are used, the upper 
corners of an ordinary rectangular tie are of httle use, and 
there is but httle, if any, objection to sawing the tie so 

as to leave off the corners, as 
shown in Fig. 20. While the 
method of triangular ties is un- 
questionably economical as to the 
number of ties which can be 
produced from given sizes of 
timber, the ties themselves are 
objectionable, since the wood is 
apt to split and check very badly, 
Fig. 20.-One tie and one ^nd the durability is very greatly 
or more planks from one diminished. Economy is also 
tree 

possible by studying the exact 

dimensions of each log to determine whether it is possible 
to cut planks from the slabs on the outside. Formerly 
the slabs were wasted. The increase in the cost of lum- 
ber has justified the effort to save them. 

no. Protection against wear by using tie-plates. — 
Although it is found that a soft-wood tie is more easily 
impregnated with chemicals, and thereby insured against 
rapid decay, the tie is not thereby protected against 
mechanical wear of the rail on the tie. This wear is largely 
prevented by use of tie-plates. Tie-plates originally had 
a flat lower surface, but, since the plates were made 
very thin, it was found that they buckled under the 
pressure of the rail. It was then thought necessary to 
use some form of corrugation or prong which should 
fasten the tie-plate in the tie. It has been found that 
even these corrugations will not secure the plate solidly 



174 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

to the tie, but that the plate will rock on the tie with 
the movement of the rail, thereby enlarging the hole 
made by the corrugation or prong. It has been found 
in many cases that this actually led to abnormal wear and 
decay immediately under the tie-plate, which caused 
the removal of the tie when it was otherwise perfectly 
sound. On this account the Southern Pacific and the 
Pennsylvania Railroads, as well as most European rail- 
roads, have adopted tie plates which have no corruga- 
tions or prongs on the lower surface. 

During recent years experiments have been made on 
European railroads, and to some extent in this country, 
-on the use of very thin strips of creosoted wood, which 
are placed immediately under the rails. These strips are 
as wide as the base of the rail, as long as the width of 
the tie, and not more than J inch thick; sometimes they 
are as thin as J inch. They are very cheap and can readily 
be renewed. The theory of their advantage is based on 
the fact that the inevitable wave-motion of the rail on 
the tie results either in the rail sliding over the tie-plate 
or in the tie-plate rocking over the tie. As long as the 
tie-plate rigidly retains its hold on the tie there is httle 
or no trouble; but when the tie-plate becomes loose, then 
it moves on the tie and wears it as has been described. 
The wooden tie-plate will invariably stick to the wooden 
tie and the rail will slide over the tie-plate. The wear 
then consists entirely of that due to the rail sliding 
over the tie-plate, and this results merely in wearing out 
the wooden tie-plate, which is reachly and cheaply 
renewed. 

III. Use of screw-spikes. — The ordinar}^ track-spikes 
are very largely responsible for the removal of ties, since 
they induce decay around the spike-hole even if the tie 
is not spike-killed by the frequent re-driving of spikes. 
Even the treated ties are ruined by the spikes, especially 



TRACK ECONOMICS. 



175 



when the ties have been treated with a chemical which 
is soluble in water, since the water will soak into the 
spike-hole and leach the chemical, which then leaves the 
wood-fibers unprotected and subject to 
decay. The best substitute for spikes, 
and the method which has been fre- 
quently adopted, is the screw-spike. 
Although the details of their design as 
adopted by various roads have a con- 
siderable variation, they all agree es- 
sentially in having a length of about 
five or six inches; have a square or 
hexagonal head so that they can be 
screwed with a suitable wrench; they 
taper to a blunt point, and have a 
screw-thread similar to those used for 
any wooden screw. Of course one es- 
sential to the form of the head is that 
it shall have a fiange wide enough to 
extend over the base of the rail and 
t aus hold it down. It is essential that a 
hole, somewhat smaller than the diam- 
eter of the spike, shall be previously drilled into the tie. 
When a large number of screw-spikes are to be placed, the 
work is accomplished by a drilhng-machine, which not only 
does the work more accurately but with greater speed. It 
has been found by actual test that such machines can put 
in two screw-spikes while three ordinary spikes are being 
driven. Even the additional time required is much more 
than saved by the reduction in track-work made possible 
by the use of screw-spikes. Although the holding-power 
of screw-spikes, compared with ordinary spikes, varies 
with the character of the wood, the average of a large 
number of tests showed that the relative holding-power of 
screw-spikes and common spikes in white oak was as 




Fig. 21. 
Screw-spike. 



176 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

1.87 : 1, while in long-leaf pine the ratio was as 4.63 .'1. 
This shows that screw-spikes are especially advantageous 
in soft-wood ties, which are so readily subject to spike- 
killing. 

112. Use of dowels. — Another device for retarding the 
destruction of ties is the invention of a French engineer 
and consists in using a creosoted piece of wood, into which 





Fig. 22. — Wooden dowels for ties. 



the spike, which may be either a common spike or a screw- 
spike, is inserted. A cylindrical hole is first bored into 
the tie; following this a shaper cuts a screw-thread in 
the sides of the hole already bored; the wooden dowels, 
which are already provided with a corresponding screw- 
thread, are then screwed in the tie. Since the upper 
part of the dowel is conical, the dowel is readily screwed 
down until it fits the hole, and there is no danger that 
water will soak in around the dowel. After the dowel is in 
place, another machine cuts it off even with the top of the 
tie. The dowel has a hole through the center which is 
bored the proper size for the insertion of the screw-spike. 



TRACK ECONOMICS. 177 

Usually a hole the proper size is provided, even when com- 
mon spikes are to be used. It is found that the compara- 
tive resistance to displacement, both lateral and vertical, 
when dowels are used with soft-wood ties is very remark- 
able, as it very largely increases the holding-power of 
the spikes and thus retards one of the most common 
causes of tie deterioration. 



CHAPTER X. 



TRAIN RESISTANCE 



113. Classification of the various forms. — ^The various 
resistances which must be overcome by the power of the 
locomotive may be classified as follows: 

(a) Resistance and losses internal to the locomotive, which 
include friction of the valve-gear, piston- and connecting- 
rods, journal friction of the drivers, also all the loss due 
to radiation, condensation, friction of the steam in the 
passages, etc. In short, these resistances and losses are 
the sum total of the lost energy by which the power at 
the circumference of the drivers is less than the power 
developed by the boiler. 

(h) Velocity resistances, which include the atmospheric 
resistances on the ends and sides of the train, the oscilla- 
tion and concussion resistances due to uneven track, etc. 

(c) Wheel resistances, which include the rolling friction 
between wheels and the rails of all the wheels (including 
the drivers), also the journal friction of all the axles except 
those of the drivers. 

(d) Grade and curve resistances, which include those 
resistances which are due to grades and curves and which 
are not found on a straight and level track. 

(e) Brake resistances. These consist of that very con- 
siderable proportion of the power developed by the loco- 
motive, which is consumed by the brakes. 

(/) Inertia resistances. From one standpoint the energy 

178 



TRAIN RESISTANCE. 179 

expended in overcoming inertia should not be considered as 
a train resistance, since it is stored up in the train as 
kinetic energy which is afterward utihzed in doing useful 
work, or it is consumed by the application of brakes; 
but, in a discussion of the demands on the tractive power 
of the engine, one of the chief items is the energy required 
to rapidly give to a starting train its normal velocity, and 
therefore this item must be considered, since a discussion 
of train resistances is virtually a discussion of the power 
required from the locomotive to overcome all the resis- 
tances. 

114. Resistances internal to the locomotive. — These are 
the resistances which do not tax the adhesion of the 
drivers to the rails. If the engine were considered as 
lifted from the rails and made to drive a belt placed 
round the drivers, then all the power that reached the 
belt would be the power that is ordinarily available 
for adhesion, while the remainder would be that consumed 
internally by the engine. The modern locomotive testing- 
plant mounts the locomotive on a series of wheels placed 
immediately under the driving-wheels. The motion of 
the driving-wheels turns the wheels on which they rest, 
and thereby operates dynamometers which measure the 
power developed. The locomotive itself is rigidly secured 
against any horizontal motion . The power developed in the 
cylinders may be obtained by taking indicator-diagrams 
which show the actual steam-pressure in the cylinder at any 
part of the stroke. From such a diagram the average unit 
steam-pressure is easily obtained, and this average pressure 
multiplied by the length of the stroke and by the net area 
of the piston gives the energy developed by one half-stroke 
of one piston. Four times this product, divided by 550 
and multiplied by the number of revolutions per second, 
gives the ^'indicated horse-power." Even this calculation 
gives merely the power behind the piston, which is several 



180 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

per cent greater than the power which reaches the circum- 
ference of the drivers, owing to the friction of the piston, 
piston-rod, cross-head, connecting-rod bearings, and driv- 
ing-wheel journals. 

By measuring the amount of water used and turned 
into steam and by noting the boiler pressure, the energy 
possessed by the steam used is readily computed. The 
indicator-diagrams will show the amount of steam that has 
been effective in producing power in the cylinders. The 
steam accounted for by the indicator-diagrams will ordi- 
narily amount to from 80 to 85% of the steam developed by 
the boiler; the other 15 or 20% represents the loss of 
energy due to radiation, condensation, etc. The power 
consumed by the engine in frictional resistances is con- 
siderably greater when the engine is hauling a train than 
when it is merely running light. It has been estimated 
that an engine w^hen running light will consume about 
11% of the power which it will develop when it is working 
to the limit of its capacity in hauling a train, but it has 
also been determined that when it is doing its maximum 
work about 15 to 16% of the power developed by the 
pistons is consumed by the engine, leaving about 84 to 
85% for the train. This may be determined by a compari- 
son of the energy developed by the pistons, as computed 
from the indicator-diagrams, with the amount of energy 
transmitted behind the tender as measured by a dyna- 
mometer at the rear of the tender. 

115. Velocity resistances, (a) Atmospheric. — These con- 
sist of the head and tail resistances and the side re- 
sistance. The head and tail resistances are nearly con- 
stant for all trains of given velocity, varying but slightly 
with the varying cross-section of engines and cars. The 
side resistance varies with the length of the train and the 
character of the cars, whether box-cars or flats. Vestibul- 
ing the cars of passenger-trains has had a considerable 



TRAIN RESISTANCE. 181 

effect in reducing the side resistances by preventing much 
of the eddying of air-currents between the cars, although 
this is one of the least of the advantages of vestibuling. 
Atmospheric resistance is generally assumed to vary as the 
square of the velocity, and, although this may be nearly 
true, it has been experimentally demonstrated to be at 
least inaccurate. The head resistance is frequently as- 
sumed to vary as the area of the cross-section, but this has 
been definitely demonstrated to be very far from true. 
A freight-train, composed partly of flat-cars and partly 
of box-cars, will encounter considerably more atmospheric 
resistance than a train consisting exclusively of either type 
of car, other things being equal. On account of the 
extreme variation in the making-up of freight-trains no 
accurate figures regarding atmospheric resistance would 
be of much value, and this probably explains why more 
effort has not been made to obtain accurate determinations 
of this form of resistance. In the comparatively few 
experiments which have been made, the head resistance 
has been assumed to vary as the cross-sectional area and 
also as the square of the velocity. The results obtained 
by different experimenters have been so discordant as to 
be of little value. The discrepancies are due to the fact 
that both of the assumptions regarding the variation of 
the atmospheric resistances are inaccurate. 

(6) Oscillatory and concussive. — These resistances are 
considered to vary as the square of the velocity. Probably 
this is nearly, if not quite, correct, on the general principle 
that such resistances consist of a series of impacts. The 
laws of mechanics tell us that the force of impact varies 
as the square of the velocity. These impacts are due to 
irregularities in the track and to the effect of the yielding 
of the rails and ties in a ballast which is not homogeneous 
in character nor absolutely uniform in its elasticity. Even 
though it were possible to make a precise determination 



182 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

of the amount of this resistance in any particular case, 
the value obtained would only be true for that particular 
piece of track and for the particular degree of excellence 
or defect which the track then possessed. The general 
improvement in track maintenance during late years has 
had a large influeixe in increasing the possible train-load 
by decreasing the train resistance. The expenditure of 
money to improve track will give a road thus improved 
an advantage over a competing road with a poorer track 
by reducing train resistance and thus reducing the cost 
of handling traffic. Although it is almost impossible to 
determine accurately the effect of a given expenditure 
in track improvement in reducing track resistance, it is 
significant to note that the resistances per ton which were 
measured by experimenters even 25 years ago were far 
higher than those obtained on the improved tracks of the 
present day. 

ii6. Wheel resistance. — (a) Rolling friction of the wheels. 
To determine experimentally the rolling friction of wheels, 
apart from all journal friction, is a very difficult matter 
and has never been satisfactorily accomplished. Another 
practical difficulty is that the rolling resistance on a track 
is more or less intimately connected with the yielding of 
the rail, which is due not only to its own elasticity but 
to the yielding under it of the ties and ballast. Theory 
as well as practice shows that the higher and more perfect 
the elasticity of the wheel and of the surface on which it 
rolls the less will be the rolling friction. The determina- 
tion, even if it could be made, would be chiefly of theoretic 
interest. The rolling friction is only a very insignificant 
part of the total train resistance. From the nature of the 
case no great reduction of the rolling friction by any 
device is possible. The use of harder rails with higher 
elasticity would probably have some effect in reducing it, 
but this effect would be so very small that it should hardly 



TRAIN RESISTANCE. 183 

be considered in comparison with the effect of that added 
hardness and elasticity on the cost of the rails and the 
rate of rail wear. 

(6) Journal friction of the axles. The energy used up 
in this form of resistance has been studied quite ex- 
tensively by means of the measurement of the force 
required to turn an axle in its bearings under various 
conditions of pressure, speed, extent of lubrication, and 
temperature. It may be measured quite accurately by 
loading a pendulum with any desired weight and hanging 
the pendulum on to the axle. The axle is then turned at 
any desired speed of rotation, which is easily measured. 
The deviation of the pendulum from the vertical position 
gives a measure of the circumferential resistance. 

The following laws have been fairly well established: 
(1) The coefficient of friction increases as the pressure 
diminishes. (2) It is higher at very slow speed, gradually 
diminishing to a minimum at a speed corresponding to a 
train velocity of about 10 miles per hour, then slowly in- 
creasing with the speed. (3) It is very dependent on the 
perfection of the lubrication, it being reduced to J or -:^\ 
when the axle is lubricated by a bath of oil rather than 
by a mere pad or wad of waste on one side of the journal. 
(4) It is lower at high temperatures and vice versa. 

The practical effect of these laws is shown by the 
observed facts that (1) loaded cars have a far less resist- 
ance per ton than unloaded cars. (2) When starting a 
train the resistance may be as much as 16 or even 20 
pounds per ton, notwithstanding the fact that the velocity 
resistances are practically zero. At a speed of two miles 
per hour it will drop to about one-half of this figure, and 
at seven miles per hour the resistance of loaded cars will 
drop to between 4 and 5 pounds per ton. (3) The journal 
resistance is so very greatly reduced by higher tempera- 
ture (which results from the increased velocity) that it 



184 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

largely neutralizes the increase in the velocity resistances, 
and tends to make the total resistance uniform for a con- 
siderable range of low velocities, say between 7 and 35 
miles per hour. (4) As a corollary to the above, it is 
found that the resistance at any given speed, say 20 miles 
per hour, is less, if the velocity has been reduced to that 
figure from some higher velocity, than it is if the velocity 
has been increased to 20 miles per hour from a lower 
velocity. (5) It has been observed that freight-train 
loads must frequently be cut down in winter by about 10 
or 15% of the loads that the same engine can haul over 
the same track in summer. This is doubtless due chiefly 
to the reduction of temperature of the journal-bearings 
and the consequent addition to the journal resistance, in 
spite of the fact that the tractive resistance will probably 
be less over a hard frozen road-bed, provided that the 
track has been kept in uniform surface. 

Roller bearings for cars have been used to some extent. 
It has been found that they very greatly reduce the start- 
ing resistance, but that their advantages grow less and 
less as the velocity increases. The effect of the adoption 
of this device on car repairs and maintenance has not yet 
been determined on a large scale, and the ultimate economy 
is still uncertain. 

117. Grade resistance. — The amount of this may be 
computed with mathematical exactness. Since the trac- 
tive resistances are computed separately, we merely have 
to compute the tendency of the wheels to roll down the 
grade, or the resistances to pulhng them up the grade, 
which are exactly equal when the frictional resistance is 
zero or when it is otherwise provided for. Assume that a 
ball or cyUnder (Fig. 23) is being drawn up an inclined 
plane. If we represent its weight by W, as measured 
graphically by the line W in the figure, then N will measure 
the normal pressure against the plane, and G will measu'-e 



TRAIN RESISTANCE. 



185 



the force required to draw it up the plane with a uniform 
velocity. It also measures the tendency of the weight to 
roll down the plane. From similar triangles we may 
write the proportion 

G:W::h:d or G = ^. .... (1) 
In the diagram d is very much larger than c, but, as will 




Fig. 23. — Grade resistance. 

be shown, c is so nearly equal to d on all practicable rail- 
road grades that there is no appreciable error in substitu- 

But - equals 



ting c for d, and write the equation G -= 



the rate of grade. Therefore we have the very simple and 
mathematically exact relation that the grade resistance 
G = W times the rate of grade. In order to appreciate 
exactly the extent of the approximation in assuming that 
the slope distance equals its horizontal projection, the per- 
centage of the slope distance to the horizontal projection 
is given in the tabular form on page 186. Incidentally 
the tabular form show^ia the amount of error involved 
W'hen we measure with the tape lying on the ground 
instead of holding it horizontally. Since almost all 
railroad grades are less than 2% (where the error is but 
.02 of 1%) and anything in excess of 4% is unheard-of 
for normal construction, the error in the approximation is 
generally too small for practical consideration. 



186 THE ECONOMICS OF RAILROAD CONSTRUCTION. 



Grade in per cent. 


1 


2 


3 


4 


5 


Slope dist 


100.005 


100.020 


100.045 


100.080 


100 125 


hor dist. 




Grade in per cent. 


6 


7 


8 


9 


10 


Slope dist. ^^^^Q 


100.180 


100.245 


100.319 


100.404 


100.499 


hor. dist. 





If the rate of grade is 1:100, G equals T^^Xyioj i-e., 
6^ = 20 pounds per toD ; therefore, for any per cent of grade, 
(j=''(20x per cent of grade) pounds per ton. When mov- 
ing up and down grade this force G must be overcome in 
addition to all the other resistances. When moving down 
a grade the force G assists the motion, and the net force 
tending to move the car or train down the grade equals 
G minus the resisting forces. If the resisting forces are 
less than G, then the train will keep moving down the 
grade, and its velocity will increase until the added resist- 
ance to increased velocity just equals G. The train will 
then move at this uniform velocity as long as such con- 
ditions remain constant. If the resistance of a train 
averaged 6 pounds per ton for a velocity of 20 miles per 
hour and the train were started on a down grade of 0.3% 
at this velocity, then it would move indefinitely at this 
speed down such a grade. If a train were started down 
a 1% grade at a velocity of say 10 miles per hour, the 
grade force will equal 20 pounds per ton on the 1% grade. 
Under such conditions the velocity of the train would in- 
crease until the velocity resistances would equal 20 pounds 
per ton. The precise speed at which this will occur de- 
pends on whether cars are loaded or empty and on various 
other conditions which affect train resistance, but the 
velocity would probably be very high, perhaps 60 or 70 
miles per hour. Since this would be too great a speed for 



TRAIN RESISTANCE. 187 

safety with freight-cars, a 1% grade of indefinite length 
can never be operated without the use of brakes. As 
developed later in the chapters on Grade, the necessary use 
of brakes on a down grade is one of the objections to grade, 
in addition to the resistance to moving up the grade. 

ii8. Curve resistance. — It is exceedingly difficult to 
obtain experimental data showing the resistance in pounds 
per ton which is due to curvature. Mr. J. F. Aspinall, an 
English engineer, who has made many elaborate experi- 
ments on train resistance, has commented on this difficulty 
substantially as follows: When the experimental train 
enters the curve the engine encounters the additional resist- 
ance first, which decreases its velocity slightly, and the 
draw-bar pull actually diminishes instead of increases. As 
the train gradually moves on to the curve, the draw-bar 
pull increases until it will settle to some definite value 
after the entire train is on the curve; but, unless the curve 
is very long or the speed very slow, the engine will begin 
to leave the curve very soon afterward. On the track on 
which Mr. Aspinall conducted his experiments, these con- 
ditions existed to such an extent that no reliable compu- 
tations of the curve resistance were possible. 

Mr. G. R. Henderson uses the value 0.5 pound per ton 
per degree of curve. This is based on the assumption that 
the resistance varies directly as the degree of curvature. 
Although precise figures for the curve resistance are so 
scarce, it is definitely known that the total curve resistance 
does not increase as fast as the degree of curve. While 
the values given by Mr. Henderson's formula may be 
suflftciently precise for ordinary easy curvature, the appli- 
cation of such a figure to the curves of 90' radius on the 
New York Elevated road would mean a resistance due to 
curvature alone of about 34 pounds per ton. The curve 
resistance on these curves is far less than this figure. Al- 
though this is a very extreme case, it is a valuable check, 



188 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

since it shows the tendency of the increase of the resist- 
ance with an increase in the degree of the curve. This 
conclusion is also corroborated by the theoretical con- 
siderations already given, that the portion of the curva- 
ture resistance which is due to longitudinal shpping is 
absolutely independent of the radius. It is quite probable 
that the curvature resistance on sharp curves is also de- 
pendent on the velocity of the train, but, unfortunately, 
there is no experimental data by which such a conclusion 
can be definitely corroborated. 

Searles makes an allowance of 0.448 pound per degree 
of curve per gross ton of 2240 pounds. He does not state 
the derivation of the value, nor how a value is obtained 
to the third significant figure, but, considering that such 
a value is the equivalent of precisely 0.4 pound per ton of 
2000 pounds or a frictional coefficient of precisely .0002, 
it is possible that the apparently precise value may be 
based on a comparatively loose approximation. 

119. Brake resistances. — The fact that grades may be 
so steep that they cannot be safel}^ operated, w^hen mov- 
ing down the grade, without the use of brakes has been 
referred to in § 117. The energy consumed by brakes is 
hopelessly lost without any compensation. The kinetic 
energy possessed by the train is transformed into heat. 
All such energy is wasted and, in addition to this, a very 
considerable amount of steam is drawn from the boiler 
to operate the air-brakes which consume the power already 
developed. When trains are required to make frequent 
stops and yet maintain a high average speed, a considerable 
amount of power is consumed in applying the brakes. It 
has been demonstrated that engines, drawing trains in sub- 
urban service, making frequent stops and yet developing 
high speed between stops, will consume a very large pro- 
portion of the total power developed by the use of brakes. 
The brakes consume the power already developed and 



TRAIN RESISTANCE. 189 

stored in the train as kinetic or potential energy, while 
the operation of the brakes requires additional steam- 
power from the engine. It should therefore not be for- 
gotten that, in some kinds of service especially, the power 
required from the locomotive may be many times the 
amount of power which is required merely to overcome 
mere track and grade resistance. 

120. Inertia resistance. — The two forms of train resist- 
ance, which, under some circumstances, are the greatest 
resistances to be overcome by the engine, are the grade 
and inertia resistances, and fortunately both of these 
resistances may be computed with mathematical precision. 
The problem may be stated as follows: What constant 
force P (in addition to the forces required to overcome 
the grade and various frictional resistances, etc.) will be 
required to impart to a body a velocity of v feet per second 
in a distance of s feet? The required number of foot- 
pounds of energy is evidently Ps. But this work imparts 

a kinetic energy which may be expressed by -75—. Equat- 
mg these values, we have Ps = -y- , or 

P^^. (2) 

2gs 

The force required to increase the velocity from vi to V2 

W 
may likewise be stated as P^7r-{v-^ — vi^). Substituting 

in the formula the values Tf^ = 2000 lbs. (one ton), (7 = 32.16, 
and s = 5280 feet (one mile), we have 

P = . 00588 (?;22-Vi2). 

Multiplying by (5280 -^3600)2 to change the unit of veloc- 
ity to miles per hour, we have 

P = . 01267 (F22-F12). 



190 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

But this formula must be modified on account of the 
rotative kinetic energy which must be imparted to the 
wheels of the cars. The precise additional percentage 
depends on the particular design of the cars and their 
loading, and also on the design of the locomotive. Con- 
sider, as an example, a box car, 60,000 lbs. capacity, 
weighing 33,000 lbs. The wheels have a diameter of 36", 
and their radius of gyration is about 13''. Each wheel 
weighs 700 lbs. The rotative kinetic energy of each wheel 
is 4877 ft.-lbs. when the velocity is 20 miles per hour, and 
for the eight wheels it is 39,016 ft.-lbs. For greater pre- 
cision (really needless) we may add 192 ft.-lbs. as the rota- 
tive kinetic energy of the axles. When the car is fully 
loaded (weight, 93,000 lbs.) the kinetic energy of transla- 
tion for 20 miles per hour is 1,244,340 ft.-lbs.; when empty 
(weight, 33,000 lbs.) the energy is 441,540 ft.-lbs.' The 
rotative kinetic energy thus adds (for this particular car) 
3.15% (when the car is loaded) and 8.9% (when the car 
is empty) to the kinetic energy of translation. The kin- 
etic energy which is similarly added, owing to the rotation 
of the wheels and axles of the locomotive, might be simi- 
larly computed. For one type of locomotive it has been 
computed to be about 8%. The variations in design, and 
particularly the fluctuations of loading, render useless any 
great precision in these computations. For a train of 
^^empties " the figures would be high, probably 8 to 9%; 
for a fully loaded train it wall not much exceed 3%. Wel- 
lington considered that 6% is a good average to use (actu- 
ally used 6.14% for '' ease of computation"), but con- 
sidering (a) the increasing proportion of live load to dead 
load in modern car design, (5) the greater care now used 
to make up full train-loads, and (c) the fact that full 
train-loads are usually the critical loads, it would appear 
that 5% is a better average for the conditions of modern 
practice. Even this figure allows something for the higher 



TRAIN RESISTANCE. 191 

percentage for the locomotive and something for a few 
empties in the train. Therefore, adding 5% to the co- 
efficient in the above equation, we have the true equation 

P = . 0133(722 -Fi2), (3) 

in which V2 and Vi are the higher and lower velocities 
respectively in miles per hour, and P is the force required 
per ton to impart that difference of velocity in a distance 
of one mile. If more convenient the formula may be used 
thus : 

70.224 

Pi——(V2'-Vi^), .... (4) 

o 

in which s is the distance in feet and Pi is the correspond- 
ing force. 

As a numerical illustration, the force required per ton 
to impart a kinetic energy due to a velocity of 20 miles 
per hour in a distance of 1000 feet will equal 

70.224(40 0-0) 

^^= 1000 =^^^^'- 

which is the equivalent (see § 117) of a 1.4% grade. Since 
the velocity enters the formula as V^, while the distance 
enters only in the first power, it follows that it will require 
four times the force to produce twice the velocity in the 
same distance, or that with the same force it will require 
four times the distance to attain twice the velocity. 

As another numerical illustration, if a train is to increase 
its speed from 15 to 60 miles per hour in a distance of 
2000 feet, the force required (in addition to that required 
for all the other resistances) will be 

.^ 70.224(3600-225) ,.^,^,, 

P-^ 2000 =118.50 lbs. per ton. 



192 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

•This is equivalent to a 5.9% grade, and shows at once 
that it would be impossible, unless there were a very heavy 
down grade, or that the train was very light and the engine 
very powerful. 

121. Train-resistance formulae. — Train-resistance for- 
mulae are usually empirical and are based oYi one of two 
forms : 

R = c+fV- \ ^^^ 

in which R is the resistance per ton, / is a coefficient to 
be determined, V equals the velocity in miles per hour, 
and c is a constant also to be determined. Formulae of the 
second class, which include some power of V represented 
by the exponent n, usually employ the second power, but 
there are some variations even from this. These formulae 
disregard grade and curve resistances, inertia resistance, 
and the active resistance (or assistance) of the wind as 
distinct from mere atmospheric resistance. In short, they 
are supposed to give the resistance of a train moving at a 
uniform velocity over a straight and level track, there 
being no appreciable wind. It may readily be seen that, 
since grade and curvature resistances and the active pres- 
sure of the wind furnish resistances which are indefinitely 
variable, all general formulae must necessarily ignore these 
elements. The quantity c represents those elements of 
resistance which are supposed to be constant, or so nearly 
constant that their variation with velocity may be ignored. 
The journal friction and the rolling friction are generally 
considered as belonging to this class. The velocity re- 
sistances are usually assumed to vary as the square of the 
velocity, and for such formulae it only becomes necessary 
to determine the value of the coefficient / to obtain the 
value of this term. Very few resistance formulae take any 
account of any variation in train-load, whether the cars 



TRAIN RESISTANCE. 193 

are loaded or empty, and whether (in freight-trains) they 
consist entirely of box cars, of fiat cars, or a combination 
of all kinds. It is well known that all these elements have 
a very material influence on the actual train resistance, 
so much so that a formula which ignores such influences 
must be considered as very approximate. Out of a great 
multitude of formulae which have been proposed, a few 
have been selected for discussion, the formulae having 
been modified (if necessary) to bring them to a uniform 
basis for comparison, in which case R equals the total 
resistance in pounds per ton of 2000 pounds. 

(a) Baldwin Locomotive Works^ formula : 

R = S+^. (6) 

This formula has the merit of extreme simplicity, but 
since, as shown above, extreme simplicity is incompatible 
with accuracy, the most that can be claimed for such a 
formula is that it is approximately accurate for ordinary 
trains and for a considerable range of velocity. Evidently 
appreciating the fact that the formulae is not applicable 
to high velocities, the following modification has been 
suggested for velocities between 47 and 77 miles per hour : 

i^ = 1.5 + 0.27 (7) 

(b) Wellington's formulae. A very simple formulae 
ascribed to Wellington is as follows : 

2^ = 4+0.005572 (8) 

Although this formula is more simple than the formula 
immediately following, it is evidently impossible for it to 
be accurate for all conditions. Wellington devised a series 



194 THE ECONOMICS OF RAILROAD CONSTRUCTION. 



of formulae which should distinguish between the character 
of the loading, whether it was carried in box cars or flat 
cars, or whether the cars were loaded or empty. The 
formulae also allow for the variation due to the weight of 
the train. Assuming that the constants have been prop- 
erly chosen, these formulae ought to give very much closer 
results than are obtainable by any other formula here 
quoted. 



R = 



3.9 +. 00657 + 
3.9 + .00757 + 
6.0 + .00837 + 
6.0 + .01067 + 



.577 
W ' 
.647 

W ' 

.577 

' W ' 

.647 - 

W ' 



. . for loaded flat cars, 
. . for loaded box cars, 
. . for empty flat cars, 
. . for empty box cars. 



(9) 



It should, however, be noted that a train consisting partly 
of box cars and partly of flat cars will have a higher resist- 
ance than is shown by any of the above formulae (and not 
a mean value), on account of the increased atmospheric 
resistance acting on the irregular form of the train, 
(c) Barnes's formula: 



i^=4+0.167. 



(10) 



It may be noted that Barnes's formula is identical with 
Welhngton's simpler formula when the velocity is 29 
miles per hour, but gives higher values for lower velocities 
and lower values for higher velocities. 
id) Aspinall's formula: 



7^ = 2.23 + 



tt5 



56.9+0.0311L 



(11) 



TRAIN RESISTANCE. 195 

This formula declares that the resistance varies as the 
f power of the velocity, and also inserts the extra term L, 
which denotes the length of the train in feet. This con- 
stitutes another method of allowing for the variation in 
the resistance due to the loading of the train. There is 
reason, however, to doubt the correctness of the form of 
this equation, since, if the train were comparatively long 
(as it might be with a train of empties), the denominator 
of that fraction would be increased, the fraction itself 
would be decreased, and the resistance per ton would be 
less. It is well known that the contrary would be the 
case, since of two trains with the same actual gross weight, 
one consisting of loaded cars and therefore comparatively 
short, and the other a comparatively long train of empty 
cars, the short train of loaded cars will have a less total 
resistance and therefore (in this case) a less resistance per 
ton. On the other hand, a long train will have a some- 
what greater atmospheric resistance, although the differ- 
ence will not be sufficient to compensate for the reduction 
in resistance due to heavy wheel-loads. As Aspinall's 
tests were made on the basis of English rolling-stock, their 
values are hardly applicable to American practice. 

(e) Searles's formula: 
72 = 4.82+0.0053672 

0.00048 72 (weight of engine and tender)^ 

gross weight of train ' ^' ^ 

This formula does not take account of differences in the 
form of the train (whether box cars or flats) which would 
affect the atmospheric resistance. Neither does it take 
into account the relation of length to weight, or whether 
the cars are loaded or empty. Considering as before two 
trains, one of which is short and heavily loaded, and the 
other a long train of empties, the weight of engine and 



196 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

tender and the gross weight of the train might be the 
same in both cases, and 3^et the resistance per ton for the 
train of empties would be considerably higher than for 
the train of loaded cars, although this formula gives them 
the same figure. 

122. Comparison of the above formulae. — For the pur- 
poses of comparison, we will compute the train resistance 
per ton according to the above formulae for a locomotive 
weighing 130 tons and with 2043 tons behind the tender 
moving at the rate of seven miles per hour. The resist- 
ances would be as follows : 

V 
(a) Baldwin: i^ = 3 + g- = 4.16. 

(6) Wellington: E = 4 + .005572 =4.27. 

(c) Barnes: E = 4 + .167 = 5.12. 

(d) Aspinall: The formula is not strictly applicable, as 
before stated, but the comparison will be interesting. We 
will assume that the 2043 actual tons behind the tender, 
loaded two contents to one tare, consist of 44 cars. 
Assuming that the cars have a total length between coupler 
ends of 37 feet, the length of the train would be 1628 feet. 
Adding 62 feet for the engine, we would have L = 1690 
feet. The formula then becomes 

25 6 
ie = 2.23 + H^-x-^.-TT^ = 2.23 + .234 = 2.46. 
56.9+52.6 

(e) Searles: 7^=4.82+0.262+0.183 = 5.265. 

Applying Wellington's more accurate formula, and 
assuming first that the cars were loaded box cars, we 

would have 

7^ = 3.9+0.367 + 0.014 = 4.28. 

If the cars were loaded flat cars, the resistance would be 

7^ = 3.9 +0.318 +0.013 = 4.231. 



TRAIN RESISTANCE. 197 

It may be noted that these last two values agree fairly 
closely with Wellington's more general formula. The 
actual results obtained during Dennis's experiments were 
4.7 pounds, which is a fair average between the low values 
given by Baldwin and Wellington and the higher values 
given by Barnes and Searles. The value given by Aspin- 
alFs formula is apparently inapplicable. 

Comparing these formul2e for a fast passenger-train, the 
results will be given below. Assume that the train con- 
sists of six cars weighing 60,000 pounds each and that it 
is drawn by a locomotive whose total weight is 280,000 
pounds. The train has a total length of 430 feet. We 
will compute, according to these formulae, its resistance at 
50 miles per hour. 

(a) Baldwin, Eq. 7: 22 = 1.5+10 = 11.5. 
(6) Wellington: 22=4 + 13.75 = 17.75. 

(c) Barnes: 22 = 4+8 = 12. 

(d) Aspinall: 22 = 2.23+9.64 = 11.87. 

(e) Searles: 22 = 4.82+13.40 + 73.5=91.72. 

It may be noted that the first three formulae agree about 
as closely as they did for the slow freight-train, and that 
even Aspinall's formula, although based on English prac- 
tice, gives a result which is very close to the average. It 
is seen, however, that Searles's formula gives a result 
which is out of all proportion to the other results. Al- 
though the formula is stated by its author 'Ho give the re- 
sistance per ton for all trains, whether freight or passenger, 
and at any velocity under ordinary circumstances,'^ it is 
evidently inapplicable to the assumed case unless we 
admit that the other formulae are worthless. 

123. Dynamometer tests.^ — Tests to obtain the resist- 
ance of trains are usually made by placing a dynamometer 
car between the locomotive and the body of the train. 



198 THE ECONOMICS OP RAILROAD CONSTRUCTION. 

The coupler between the car and the locomotive includes 
a dynamometer attachment which automatically records 
at any instant the actual pull on the draw-bar. Appar- 
ently this ought to solve the problem very easily and 
accurately, but in practice it is found that the interpreta- 
tion of the dynamometer records is not easy and is liable 
to misconstruction, unless care is taken to make several 
allowances. One of the practical difficulties in interpret- 
ing the results of dynaniometer experiments is to deter- 
mine the actual velocity, especially when the velocity is 
not regular. Speed-recorders are supposed to indicate the 
velocity at any instant, but they are not very accurate 
even when the velocity is uniform, and they are especially 
inaccurate when the velocity is fluctuating. When the 
velocity of the train is decreasing, the kinetic energy of 
the train is being turned into work, and a force transmitted 
through the dynamometer is less than the amount of the 
resistance which is actually being overcome. Therefore, 
unless the indication of the dynamometer is carefully cor- 
rected by adding to it the force calculated according to 
formula 4, which equals the force which is really assisting 
the train when its velocity is reduced from V2 to Vi in a 
distance s, the indication of the dynamometer will not 
represent the force required to overcome the resistances 
actually encountered by the train. On the other hand, 
when the velocity is increasing, the dynamometer indicates 
a larger force than is required to overcome the resistances, 
but the excess force is being stored up in the train as 
kinetic energy. In such a case, the force Pi, calculated 
from formula 4 on the basis of the differences of velocities 
in any assumed distance s, must be subtracted from the 
dynamometer record in order to obtain the force necessary 
to overcome the train resistances. Grade has a similar 
effect, and the force indicated by the dynamometer may 
be greater or less than that required at the given velocity 



TRAIN RESISTANCE. 199 

on a level by the force ^Yllich is derived from, or is turned 
into, potential energy. Since grade, either ascending or 
descending, is usually found in the track, the actual grade 
of the road-bed must be known and allo^Yed for at ail 
points. Curvature must likewise be allowed for, as it has 
a constant retarding force. Usually the allowance per ton 
is 0.5 pound. 



CHAPTER XI. 

MOMENTUM GRADES. 

124. Velocity head. — When a train starts from rest and 
acquires its normal velocity, it overcomes not only the 
usual track resistances (and perhaps curve and grade 
resistances), but also performs work in accumulating a 
large amount of kinetic energy. Such work is not neces- 
sarily lost. In fact there need not be the loss of a single 
foot-pound of such energy, provided it is not necessary 
to dissipate the energy by the application of brakes. If 
for a moment we consider that a train runs without any 
friction, then, when running at a velocity of v feet per 
second, it possesses a kinetic energy which would raise 

v^ . 
it to a height of h feet, when h = ^, in which g is the ac- 

celeration of gravity which equals 32.16 feet per second 
in a second. Still ignoring ' friction, the train would 
climb a grade until it had attained an elevation of 
h feet above the point where its velocity was v. When 
it had climbed a height of h^ feet (less than h) it would 
have a velocity Vi=\/2g(h — h^). As an illustration 
assume that 2; = 30 miles per hour =44 feet per second. 

Then /i = 77- = 30.1 feet. Still assuming that there is no 

friction, the kinetic energy in the train would carry it up 
a grade until it had attained an elevation of 30.1 feet, or 

200 



MOMENTUM GRADES. 201 

it would carry it for two miles up a grade of 15 feet per 

mile or half a mile up a grade of 60 feet per mile. When 

the train had climbed 20 feet there would still be 10.1 

feet left of velocity head, and its velocity would be 

v = V2g{10.1) =25.49 feet per second = 17.4 miles per hour. 

But these figures must be slightly modified, on account of 

the revolving-wheels, of the train, as already discussed in 

§ 120. When train velocity is being acquired part of the 

work done is spent in imparting the energy of rotation to the 

driving-wheels and various truck-wheels of the train. Since 

these wheels run on the rails and must turn as the train 

moves, their rotative kinetic energy is just as effective (so 

far as it goes) in being transformed back into useful work. 

The proportion of this rotative energy to the kinetic 

energy of translation has already been computed in § 120, 

in which the corrective value of 5% has been adopted. 

5280 
Since v equals ^^tjtt V = 1 .4667 V, in which v equals the 

velocity in feet per second and V equals the velocity in 
miles per hour, and since v^ equals 2.151 V^ we may write 
Velocity head 

v^ in ft. per sec. 2.1517^ in m. per h. nQQ/t/LT72 
^ 64:32 ^ 64:32 =0.03344K 

Adding 5% for the rotative kinetic energy of 

the wheels =0.0016772 



The correct velocity head therefore =0.035117^ 

On account of the great usefulness of these values, as 
explained later, the velocity-head for velocities varying 
from 10 to 50 miles per hour have been computed as shown 
in Table XX. Part of these figures were obtained by 
interpolation, and the final hundredth may be in error 
by one unit, but it may readily be shown that the final 



202 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

hundredth is of no practical importance. It is also true 
that the chief use made of this table is with velocities 
much less than 50 miles per hour. 

125. Practical use of Table XX. — The previous demon- 
stration has been made under the assumption, many times 
repeated, that the frictional resistances to the movement 
of the train are zero. The same law will hold if we may 
assume that the engine is doing an amount of work which 
at all times is just equal to that required to overcome 
such resistances. It has been found that the tractive 
resistances (which here include all resistances except those 
due to grade) are nearly independent of velocity for a 
very considerable range of velocity, which includes the 
most common freight-train velocities. It is also assumed 
that the draw-bar pull is uniform for these various veloc- 
ities. This last assumption is virtually the same as assum- 
ing that the tractive power of the drivers is independent 
of velocity, and that the engine is capable of varying 
its output measured in horse-power indefinitely. None 
of these assumptions are strictly true, but a thorough 
appreciation of this method of calculation will assist very 
materially in studying the value and use of momentum 
grades, since the error is practically inappreciable when 
operating small sags and humps, and does not become of 
very great value except in extreme cases. We will first 
apply the method to some practical cases on the basis, as 
before stated, that the tractive resistances are independent 
of velocity, and that the pull on the draw-bar of the loco- 
motive is constant. Assume that a train is passing A 
(see Fig. 24) running at a velocity of 15 miles per hour. 
Assume that the throttle is not changed nor any brakes 
applied, and that the engine is capable of increasing its 
horse-power, so that, in spite of its increased velocity on 
the succeeding down grade, it is still able to exert the same 
draw-bar pull. At A its velocity head is that due to 



MOMENTUM GRADES. 



203 



Table XX. — Velocity Head (representing the Kinetic Energy) 
OF Trains moving at Various Velocities. 



Velocity 
m. per h. 



0.0 



3.51 
4.25 
5.06 
5.93 
6. 



0.1 



7.90 

8.99 

10.15 

11.38 

12.68 



14.05 
15.49 
17.00 

18.58 
20.23 



21.95 
23.74 
25.60 
27.53 
29.53 



3.58 
4.33 
5.15 
6.02 
6.98 



0.2 



8.00 

9.10 

10.27 

11.50 



3.65 
4.41 
5.23 
6.12 

7.08 



12.81 12.95 



14.19 
15.64 
17.15 
18.74 
20.40 



22.12 
23.92 
25.79 
27.73 
29.73 



31.60 31.81 
33.74|33.96 
35.95 36.17 



38.23 
40.58 



43.01 
45.51 
48.08 
50.72 
53.42 



56.19 
59.03 
61.94 
64.92 
67.98 



71.10 
74.30 

77.57 
80.91 
S4.32 
87.79 



38.46 
40.82 



43.26 
45.76 
48.34 
50.99 
53.69 



56.47 
59.32 
62.23 
65.22 

.29 



71.42 
74.62 
77.90 
81.25 
84.66 
88.14 



8.11 

9.21 

10.39 

11.63 



0.3 



3.72 
4.49 
5.32 
6.21 
7.19 



0.4 



3.79 
4.57 
5.41 
6.31 

7.29 



8.22 8.33 
9.32 9.43 



0.5 



3.87 
4.65 
5.50 
6.40 
7.39 



0.6 



14.33 
15.79 
17.30 
18.90 
20.57 

22.30 
24.10 
25.98 
27.93 
29.93 



32.02 
34.18 
36.39 
38.69 
41.06 



43.51 
46.01 
48.60 
51 . 26 
53.96 



56.75 
59 . 61 
62.52 
65.52 
88.60 



71.74 
74.94 
78.23 
81.59 
85.00 
88.49 



10.51 
11.76 
13.08 



14.47 
15.94 
17.46 
19.06 
20.74 



22.48 
24.28 
26.17 
28.13 
30.13 



32.23 
34.40 
36.62 
38.92 
41.30 



43.76 
46 ."^6 
48.86 
51.53 
54.23 



57.03 
59.90 

62.82 
65.82 
.91 



72.06 
75.26 
78.56 
81.93 
85.34 
88.85 



10.63 
11.89 
13.22 



14.61 
16.09 
17.62 
19.22 
20.91 



22.66 
24.46 
26.36 
28.33 
30.34 



32.44 
34.62 
36.85 
39.15 
41.54 



44.01 
46.52 
49.12 
51.80 
54.51 



57.31 
60.19 
63.12 
.12 

.22 



72.38 
75.59 

78.89 
82 . 27 
85.69 
89.20 



8.44 

9.55 

10.75 

12.02 

13.35 



14.75 
16.24 

17.78 
19.38 
21.08 



22.84 
24.65 
26.55 
28.53 
30.55 



32.65 

34.84 

37. 

39.38 

41.78 



44.26 
46.78 
49.38 
52.07 
54.79 



57.59 
60.48 
63.42 
.43 
69.53 



72.70 
75.92 
79.22 
82.61 
86.04 
.55 



3.95 

4.73 
5.58 
6.50 

7.49 



8.55 

9.67 

10.87 

12.15 

13.49 



14.89 
16.39 
17.94 
19.55 
21.25 



23.02 

24.84 
26.74 
28.73 
30.76 



32.86 
35.06 
37.31 
39.62 
42.02 



44.51 
47.04 
49.64 
52.34 
55.07 



57.87 
60.77 
63.72 
.74 
.84 



73.02 

76.25 
79.55 
82.95 
.39 
89 . 91 



0.7 



4.02 
4.81 
5.67 
6.59 
7.60 



8.66 

9.79 

10.99 

12.28 

13.63 



15.04 
16.54 
18.10 
19.72 
21.42 



23.20 
25.03 
26.93 
28.93 
30.97 



33.08 
35.28 
37.54 
39.86 
42.26 



44.76 
47.30 
49.91 
52.61 
55.35 



58.16 
61.06 
64.02 
67.05 
70.15 



73.34 
76.58 
79.89 
83.29 
86.74 
90.26 



4.10 

4.89 
5.75 

o.ec 

7.70 



8.77 

9.91 

11.12 

12.41 

13.77 



15.19 
16.62 
18.26 
19.89 
21.59 



23.38 
25.22 
27.13 
29.13 
31.18 



33.30 
35.50 
37.77 
40.10 
42.51 



45.01 

47.56 
50.18 
52.88 
55.63 



58.45 
61.35 
64.32 
67.36 
70.46 



73.66 
76.91 
80.23 
83.63 



0.9 



4.17 
4.97 
5.84 
6.78 
7.80 



10.03 
11.25 
12.55 
13.91 



15.34 
16.84 
18.42 
20.06 
21.77 



23.56 
25.41 
27.33 
29.33 
31.39 



33.52 
35.72 
38.00 
40.34 
42.76 



45.26 
47.82 
50.45 
53.15 
55.91 



58.74 
61.64 
64.62 
67.67 
70.78 



73.98 

77.24 
80.57 
83.97 



87 . 09 87 . 44 
90.6190.97 



204 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

15 miles per hour or 7.90 feet. At B it has gained 20 feet 
more, and its velocity is that due to a velocity head of 
27.90 feet, or nearly 28.2 miles per hour. Upon climbing 
the grade BC, when it reaches the point B^, it has given 
up its velocity head, due to the additional 20 feet, and its 
velocity head is again 7.90. At the point C, which is 4 
feet higher than B^, its velocity head is only 3.90, which 





Virtual Profile 




• Train vel. 10.5 m. pert. 


n vel. 15^m..perh. 1 A 




1^ 


B ^^T ^^'^^^'rrrrnrrl^' Train^vel. 15 m. per 


jfjj ■ '•ij)>lliiiiiiiiiiiiiiiiitiillllli/////j/i//- 



Fig. 24. — ^Relation of virtual and actual profile through a sag 
and over a hump. 



corresponds to a speed of about 10.5 miles per hour. As 
the train starts down the grade CD its velocity continues 
to increase from 10.5 miles per hour, and when it has 
reached C it has again recovered the 4 feet of velocity 
head and will again be moving at the velocity of 15 miles 
per hour. If at this point the grade again becomes level, 
the train will continue to move on as before at a velocity 
of 15 miles per hour. It will have been practically unin- 
fluenced by the presence of the combined sag and hump. 

126. Accuracy of the above statement. — The late A. M. 
Wellington, in giving a detailed solution of a problem 
substantially like the above, declared that he had taken 
velocity and dynamometer records in hundreds of cases 
of trains that were operated substantially as above, and 
that he had found that for all practical purposes the draw- 
bar pull was constant, whether the velocity was great or 
small, and that the velocity at the foot of the sag or at 
the summit of the hump was substantially in accordance 



MOMENTUM GRADES. 205 

with the theoretical figures obtained for the particular case. 
In a paper read before the American Society of Civil 
Engineers on December 3, 1902, by Mr. A. C. Dennis, the 
statement was made that, as a result of tests aggregating 
thousands of miles of train operation, he found that 
freight-train resistance, when duly corrected for existing 
curvature and grade and for change in velocity, was sub- 
stantially a uniform quantity at about 4.7 pounds per ton 
for loaded trains between the velocities of 7 and 35 miles 
per hour. Since the velocities in the above example 
are well within these limits, there would be little or no 
error due to variation of tractive resistances. Assimie 
that -the train in the above problem weighs 1500 tons. 
Let us assume that it approached the point A on a level 
track, and that it was moving at a velocity of 15 miles 
per hour, which is at the rate of 22 feet per second. 
Assuming that the tractive resistance is 4.7 pounds per 
ton, we would have, as the total horse-power developed 
at the speed of 15 miles per hour, 

1500x4.7x22 



550 



= 282 H.P. 



According to the assumption of a uniform draw-bar pull, 
when the train reached the bottom of the sag it would 
be moving at a velocity of 28.2 miles per hour, and it 
must therefore be developing 530 H.P. When it has 
moved up the succeeding grade and has reached the 
summit of the hump, the velocity is assumed to be 10.5 
miles per hour instead of 15, and the horse-power re- 
quired at this velocity will be only 197.4. Although 
the horse-power developed by a locomotive may vary be- 
tween rather wide limits, the range of this variation is 
subject to definite limitations. At a very low velocity 
the tractive power is absolutely limited by the frictional 
resistance between the driving-wheels and the rails. Al- 



206 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

though the coefficient of friction will not ordinarily exceed 
25%, there are some cases where, by the use of sand, a 
coefficient approximating one-third may be obtained. 
Therefore the weight on the drivers multiplied by 25% is 
usually a limiting measure of the tractive power of the 
locomotive. At very low velocities the maximum horse- 
power of the locomotive is therefore limited by the prod- 
uct of the maximum tractive power and the velocity 
which the locomotive can develop. At some speed, which 
is usually over 10 to 15 miles per hour, it not only becomes 
impossible for the locomotive to develop steam fast enough 
to supply the cylinders at full stroke, but it also becomes 
far more effective to use the steam expansively. The 
maximum tractive force which can be developed by an 
engine for one complete revolution of a driver equals 
Theoretical tractive force 

(diam. piston) Xav. steam-pr. X stroke 
~ diameter of drivers 

The effective steam-pressure is considerably less than 
this, and none of the above quantities are variable except 
the pressure. If the effective steam-pressure in the cylin- 
der is reduced, as must be the case when the steam is used 
expansively, then the effective tractive power is unques- 
tionably reduced. In spite of the reduction in effective 
steam-pressure, it is possible that the speed may become 
so high that the horse-power developed is greater, in spite 
of the reduced draw-bar power, than it was before. Never- 
theless, the draw-bar pull certainly does decrease with 
increased velocity. The speed at which it will begin to 
decrease depends on the ability of the boiler to develop 
steam rapidly. In Fig. 26 is shown in a diagram the reduc- 
tion in tractive power with increase of velocity of the 
consolidation locomotive with which Mr. A. C. Dennis 
made the tests above referred to. It will be noticed in 



MOMENTUM GRADES. 



207 



this particular case that the draw-bar pull commenced to 
decrease immediately, and that at 14 miles per hour the 
tractive force had reduced to 75%. 

127. Utilization of Table XX. — Locomotive engineers 
very soon learned to utilize the advantage of ^'a run at 
the hill," and found that whenever they were able to 
approach a hill with a high velocity they would be able 
to draw up that hill a considerably heavier train than 
could be hauled if they started from rest or at a low veloc- 
ity at the bottom of the hill. This advantage, however, 
is limited by the length of the hill, and it really becomes a 
question of the difference of elevation which can be sur- 
mounted by virtue of the kinetic energy stored in the 
train when it reaches the bottom of the hill. As the train 



(a) Hump in track otherwise level. 




(&) Hump on a grade otherwise unifonn. 




(c) Sag on a grade otherwise uniform. 
Fig. 25. — Sags and humps on grades otherwise uniform. 



climbs the hill and its velocity diminishes, the tractive 
force will increase rather than diminish, the tractive re- 
sistance will diminish rather than increase (assuming that 



208 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

the velocity does not decrease to less than 7 miles per 
hour), and therefore the kinetic energy can all be utilized 
in overcoming the elevation. About the only exception 
to this occurs when a freight-train has been forced to attain 
such a high velocity at the bottom of a hill that the reserve 
boiler-power has been overtaxed, and the boiler-pressure 
falls because the boiler is unable to produce steam with 
sufficient rapidity, but this wdll be largely a matter of the 
way the engine is handled. In a very simple case, such 
as the mere insertion of a hump either on an otherwise 
level track or on an otherwise uniform grade, such as is illus- 
trated in Fig. 25 (a) or (b), whenever we can rely on a 
-train reaching that hump with a sufficient velocity, and 
with the engine doing an amount of work which would 
carry it along the uniform grade at that velocity. Table 
XX will show whether that hump can be surmounted so 
that the velocity at the summit of the hump will still be 
within practicable limits, say 10 miles per hour. The 
other case (c) in Fig. 25 cannot always be determined 
accurately by this table, although the table may be de- 
pended on to give an approximate result, unless the case 
is very extreme. If a sag is very deep, one of several 
things may happen. First, the velocity at or near the 
bottom of the sag may become so great that steam must 
be shut off and brakes applied in order to prevent the 
train from attaining an objectionably high velocity. In 
such cases the table is not supposed to apply, since an 
express condition of the table is that the tractive force 
exerted by the engine is uniform. Second, even if it is 
attempted to operate the engine so that the tractive force 
is uniform, it may become impossible, as explained above, for 
the boiler to make steam fast enough to develop such power. 
If that full amount of power is not developed at the bottom 
of the sag, then the full amount of kinetic energy will not 
be developed, which will be necessary to permit the train 



MOMENTUM GRADES. 209 

to surmount the steeper grade and reach the upper end of 
the sag with its original velocity. Whether this will be 
the case can best be determined by means of momentum 
diagrams, such as will be described later. 

Momentum Diagrams and Tonnage Ratings. 

128. Tonnage rating. — The following demonstration is 
based very largely on the admirable paper by Mr. A. C. 
Dennis, M. Am. Soc. C. E., which has been previously re- 
ferred to. The paper as originally presented is very much 
condensed, and is not easy to be understood by those who 
have little or no know^ledge of the subject. The state- 
ments and numerical illustrations have therefore been 
amplified in the endeavor to present a somewhat difficult 
subject in a simple form. 

129. Tonnage rating of locomotives. — Dennis's experi- 
ments indicated that the draw-bar pull of the particular 
locomotive tested, after being corrected for inertia, grade, 
and curvature, when drawing a train of empty box cars, 
averaged about 8.9 pounds per ton. The variation from 
this figure between the velocities of 7 and 30 miles per hour 
did not exceed 0.1 pound per ton. On the other hand, the 
tractive resistance to loaded cars was very uniform at 4.7 
pounds per ton when the 'Hare-weight," or weight of the 
empty cars, w^as one-third of the total weight. Since 
train-loads are made up of loaded, partially loaded, and 
empty cars, the only practicable method of uniform ton- 
nage rating is to equate live load and tare-weight to a 
uniform basis of resistance. Since empty cars showed a 
resistance of 8.9 pounds per ton, and since the resistance 
per ton was lowered to 4.7 when the cars were loaded with 
a live load twice the tare-w^eight, we may write an equa- 
tion as follows, in which R = the resistance in pounsd per 
ton due to the live load, 



210 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

7^XH-8.9XJ = 4.7, 

from which we may derive R = 2.6. The reasonableness 
of this view becomes more apparent when we consider that 
the total tractive resistance consists of the summation of 
several resistances, some of which (such as atmospheric 
resistance) are independent of weight, and some of which 
(such as axle resistance) are decreased per ton by an increase 
in weight. 

According to the above figures, a 50-car train of empties, 
weighing 15 tons each, would have a tractive resistance of 
50x15x8.9=6675 pounds. If each car was loaded with 
15 tons, we would have an additional tractive resistance of 

50x15x2.6 = 1950 pounds, 

or a total of 8625 pounds. Loading on 15 more tons per 
car would add another 1950 pounds, making a total of 
10,575 pounds. But the total tonnage would then be 
2250 and the average resistance would be 4.7 pounds per 
ton. The tonnage rating is then given by multiplying the 
tare-weight by a factor such that the '^rating ton," as it 
is called, multiplied by 2.6 will equal the actual tare- 
weight resistance per ton. But since the grade resistance 
per ton is a definite quantity, we cannot use the increased 
hypothetical equivalent in tons in allowing for the actual 
grade resistance. This factor therefore depends on the 
rate of grade. For example, on a 0.4% grade the tractive 
resistance for a ^'rating ton " is 2.6 pounds; the grade 
resistance is 8 pounds, the total is 10.6. A ton of tare has 
a resistance of 9.0 and has a grade resistance of 8.0, or a 
total of 17. This is 160% of a rating ton. The corre- 
sponding figures for other grades are as given in Table 
XXI. 

In Fig. 26 is shown the actual tractive power of the 



MOMENTUM GRADES. 



211 



Table XXI. — Ratio of Tare Tons to Rating Tons for Various 

Grades. 



Grade in 
percent. 


0.0 


0.1 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


1.0 


Tare ton 
Rating ton 


346% 


239% 


197% 


174% 


160% 


151% 


144% 


139% 


134% 


131% 


128% 


Grade in 
per cent. 


1.0 


1.1 


1.2 


1.3 


1.4 


1.5 


1.6 


1.7 


1.8 


1.9 


2.0 


Tare ton 
Rating ton' ' 


128% 


126% 


124% 


123% 


121% 


120% 


118% 


117% 


117% 


116% 


115% 



locomotive used in Mr. Dennis's tests. The curve of trac- 
tive power was obtained by adding to the actual dyna- 
mometer pull the grade and rolling resistance of the loco- 
motive and tender. The curve represents average values; 
the maximum values were about 1000 pounds higher. 

130. Tonnage rating for a given grade and velocity. — 
We will first compute the tonnage rating for this locomo- 
tive on the basis of a velocity of 7 miles per hour and for 
a 0.4% grade. The tractive power, as obtained from Fig. 
26, for this speed is 28,200 pounds. The grade and tract- 
ive resistance for a rating ton on this grade is (8.0+2.6) 
or 10.6 pounds per ton. At 7 miles per hour, the locomo- 
tive could therefore handle (28,200 --10.6) or 2660 gross 
rating tons. The actual weight of the locomotive and 
tender was 130 tons. On a 0.4% grade this is the equiva- 
lent of (160% X 130) =208 rating tons, which leaves 2452 
rating tons behind the tender. The actual load behind 
the tender will depend on the character of the car loading. 
Assume first that all cars were empty, then the actual 
loading would be 2452 -1.60 = 1529 tons. If the live load 
exactly equaled the tare, we would have for each two 
tons one ton of live load and (1x1.60) rating tons of 

2 
tare. The actual tonnage would be ^ ^^. X 2452 = 1886 



f' ( 



212 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

tons. If the live load is twice the tare, the actual tonnage 

3 
would be ^-—j-x^X 2452 =2043 tons. The above calcula- 
tions are on the basis of 7 miles per hour. If the speed 
were increased to 25 miles per hour, the tractive power 





s-^ . 
































30000 


::^we- 


^ 


Sf^'-Zn, 
























30000 




"^ 




V 
































N 


V. 




































V 


'^u 


















I 
1 


ofinoo 
















'^''1 














or\f\[\(\ 


















\ 


































\ 


\ 






















Cou 


p. CO 


isol. 


oco. 








\ 














10000 






Locp.weii 
Tender 


.' -1 


50025 

09025 










^ 


\^ 


x^ 




10000 








Tot 
On( 


irive 


" -2 
■s -1 


59050 
53400 














"\ 














































































































3 ■ 


i 


> 


1 





1 


5 


2 





2 


5 


a 





a 


5 



Sj)eed.in miles Eeciouy 



Fig. 26. — Locomotive tractive power curve. 



of the locomotive is considerably less. According to 
Fig. 26 it is only 12,900 pounds. Dividing this as 
before by 10.6 we have 1217 rating tons. Subtract- 
ing the 280 rating tons for the locomotive and tender, 
we have left 1009 rating tons for the cars. As before, 
w^ would havQ 



MOMENTUM GRADES. 



213 



1009 Xj—T-gQ = 776 tons for half loading, 
3 



1009 X. 



= 842 



and 



2+1.60 
1009-1.60 =631 '' '' 



fuU '' 
empties. 



A tabulation of the above values will more clearly indicate 
the comparative effect of grades and loading. It is 
assumed that ^'full load " means a live load of double the 
weight of the car. 



Velocity of train. 


Cars empty. 


Half loaded. 


Fully loaded. 


7 miles per hour 


1529 
631 


1886 
776 


2043 


25 " " " ' 


842 







The reduction in the capacity of the locomotive at the 
higher speed is not due to the extra resistance, but to the 
inability of the locomotive to develop the requisite power 
at the higher rate. 

131. Acceleration curves. — If we divide the total trac- 
tive power by the gross rating tonnage, we will have the 
available power in pounds per ton. If we subtract from 
this the tractive resistances, including grade resistance and 
the resistance due to curvature, the remainder will be the 
force which is available for acceleration. If these resist- 
ances are more than the available power per ton, the 
difference will be negative and will indicate a retarding 
force. 

On the same principle as used in computing gravity 
resistance (§ 117), we may say that a given accelerative 
force per ton will be able to alter the potential head (or 
velocity head) by a proportional amount in a given dis- 
tance. If P = the accelerating force per ton, then 

P:2000::(/i?-/ii):s, 



214 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

in which /12 and hi are the two velocity heads and s the 
distance. If we say that h=0m5llV^ (see § 121), and 

substitute for Vi and V2 in Eq. 4 (§ 120) the values k^ti 

and -JAoFTT? we will have 

_, 2000,, , , 2000., , , ^^ .. 

^=-^-(^2-/^1), or s = ~-p-{h2-hi)y . (14) 

which is the same as the above equation. If our accel- 
erating force is, say, 10 pounds per ton, then the distance 
required for a change of one foot of velocity head will be 

^« or 200 feet. 

Assume that the consolidation locomotive which we 
have been discussing is loaded with a train-load of 2452 
rating tons behind the tender, which is the capacity of 
that locomotive running for an indefinite distance at 7 
miles per hour up a 0.4% grade. This loading (2452 rating 
tons) might be made up of an indefinite number of com- 
binations of empty cars, loaded cars, or loaded and empty 
cars. The train having been started out from the ter- 
minal with this loading, we wish to compute its probable 
behavior on other grades and at different velocities. We 
will first study its behavior on a level grade. Since it is 
working in a manner which would carry the train up a 
0.4% grade at 7 miles per hour, it will evidently gain 
velocity on the level grade. The total weight of train and 
engine is 2660 rating tons, on which the resistance due to 
traction is only 2660x2.6 = 6916 pounds. The tractive 
power of this engine at various velocities is as shown in 
the diagram Fig. 26. The tractive power for each velocity 
in miles per hour is as given in Table XXII. For example, 
at 10 miles per hour the tractive power is 26,400 pounds. 
Subtracting from this the power required for tractive 



MOMENTUM GRADES. 215 

resistance, which we will call 6900 for a round number, 
we will have 19,500 pounds available for acceleration. 
The velocity head at 10 miles per hour (as taken from 
Table XXII) is 3.51; for 9 miles per hour it is 2.84. The 
difference is .67 foot. The total weight of our train in 
rating pounds equals 5,320,000. Therefore the distance 
required to increase the velocity from 9 to 10 miles per 
hour equals (see Eq. 6) 

5,320,000 

which means that the tractive power of the engine is such 
that it would increase the velocity of that train from 
9 to 10 miles per hour in a distance of 183 feet. This 
figure, 183, is found in Table XXII in column 6, opposite 
the velocity of 10 miles per hour in column 1. The other 
numbers of column 6 are similarly obtained. The num- 
bers of column 7 are obtained in each case by adding the 
sum of all the distances from zero, as given in column 6, 
and give the total distance from the origin that must be 
traveled before the locomotive working in that manner 
will attain the velocity as given in column 1. Considering 
the numbers in column 7 as ordinates, we may plot the 
acceleration curve marked ^' level " in Fig. 27. 

To determine the behavior of this train on other grades, 
we will apply this same method to determine the other 
acceleration curves as given in Fig. 27. For example, the 
tractive power required of the locomotive at 7 miles per 
hour on a 0.4% grade is 28,200 pounds. At 5 miles per 
hour the tractive power of the engine is 29,100 pounds, 
and therefore the surplus is only 900 pounds (as given in^ 
column 8). The distance required for the difference of 
velocity head between 4 and 5 miles per hour, com- 
puted as before, equals about 1890 feet. Working out the 



l?9j ni ooTirtiRid 







MOMENTUM GRADES. 217 

other distances similarly, we would have the other numbers 
in column 9, and adding these partial distances we have 
the sum totals as given in column 10. It should be remem- 
bered, however, that this curve has but little value, since 
the computations depend on the assumption of a uniform 
resistance per ton, which is far from being true with very 
low velocities. The form of the curve, however, is very 
instructive, since it shows that when it is running up the 
4% grade with a velocity less than 7 miles per hour its 
surplus accelerative power is very small; it must neces- 
sarily run a long distance before its velocity will materially 
increase, and theoretically it will require an infinite time 
to quite reach the velocity of 7 miles per hour. Speaking 
mathematically, the curve (+0.4) is asymptotic to the 
vertical line over 7. 

In Table XXII the ordinates for the lowest of the accel- 
eration curves ( — 1.0) has been worked out in columns 11, 
12, and 13. In this case each rating ton assists the tract- 
ive power by a force of (20.0 — 2.6), or 17.4 pounds per 
ton. This makes a total added power of 46,284 pounds, 
which we call 46,300 for round numbers. Adding this 
constant to the tractive power of the locomotive, we have 
the net tractive power available for acceleration as shown 
in column 11. Applying these values similarly, we obtain 
the comparative short distances required to change the 
velocity heads by the amounts given in column 4, and in 
column 13 we have the total distance required to attain the 
given velocities. 

132. Retardation curves. — ^When the train has succeeded 
in acquiring a high velocity on a favorable down grade 
and then strikes an up grade, it will be unable to maintain 
that high velocity, and its velocity will gradually decrease. 
The distance required for the decrease from one velocity 
to another will be as given by the retardation curves shown 
in Figs. 27, 28, and 29. For example, if the train has 



218 THE ECONOMICS OF RAILROAD CONSTRUCTION. 



Table XXII. — Determination of Coordinates of Velocity- 
distance Curves for One Type of Locomotive. 



M 






1 


Operating on level. 


Operating on 
+ 0.4% grade. 


Operating on 
-1.0% grade. 




1 


i 

>> 






1! 


i 
1 


o - 




8 

G 


1 » 

m 


o 

'*^ to 

;:: o 


1 


1 

1 


■!3 ;3 


1 
3 


is 

ft 




ft 


-3 
1 


III 


5o| 

ft 


H 


1^" 


r 


1 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


1 


30,300 


.03 


0.035 


23,400 


8 


8 


2,100 


90 


90 


76,600 


2 


2 


2 


30,000 


.14 


.105 


23,100 


24 


32 


1,800 


310 


400 


76,300 


7 


9 


3 


29,800 


.32 


.18 


22,900 


42 


74 


1,600 


600 


1,000 


76,100 


13 


22 


4 


29,500 


.56 


.24 


22,600 


56 


130 


1,300 


980 


1,980 


75,800 


17 


39 


5 


29,100 


.88 


.32 


22,200 


77 


207 


900 


1,890 


3,870 


75,400 


23 


62 


6 


28,700 


1.26 


.38 


21,800 


91 


298 


500 


4,040 


8,910 


75,000 


27 


89 


7 


28,200 


1.72 


.46 


21,300 


115 


413 








74,500 


33 


122 


8 


27,600 


2.25 


.53 


20,700 


136 


549 








73,900 


38 


160 


9 


27,000 


2.84 


.59 


20,100 


156 


705 








73,300 


43 


203 


10 


26,400 


3.51 


.67 


19,500 


183 


888 








72,700 


49 


252 


11 


25,700 


4.25 


.74 


18,800 


209 


1,097 








72,000 


55 


-307 


12 


24,900 


5.06 


.81 


18,000 


239 


1,336 








71,200 


60 


367 


13 


24,000 


5.93 


.87 


17,100 


270 


1,606 








70,300 


66 


433 


14 


23,100 


6.88 


.95 


16,200 


312 


1,918 








69,400 


73 


506 


15 


22,200 


7.90 


1.02 


15,300 


355 


2,273 








68,500 


79 


585 


16 


21,200 


8.99 


1.09 


14,300 


405 


2,678 








67,500 


86 


671 


17 


20,100 


10.15 


1.16 


13,200 


467 


3,145 








66,400 


93 


764 


18 


19,000 


11.38 


1.23 


12,100 


541 


3,686 








65,300 


100 


864 


19 


17,900 


12.68 


1.30 


11,000 


628 


4,314 








64,200 


108 


972 


20 


16,800 


14.05 


1.37 


9,900 


737 


5,051 








63,100 


115 


1,087 


21 


15,700 


15.49 


1.44 


8,800 


870 


5,921 








62,000 


123 


1,210 


22 


14,900 


17.00 


1.51 


8,000 


1,004 


6,925 








61,200 


131 


1.341 


23 


14,100 18.53 


1.58 


7,200 


1,167 


8,092 








60,400 


139 


1,480 


21 


13,400 20.23 


1.65 


6,500 


1,350 


9,442 








59,700 


147 


1,627 


25 


12,900121.95 


1.72 


6,000 


1,524 


10,966 








59,200 


154 


1,781 


26 


12,400 23.74 


1.79 


5,500 


1,730 


12,696 








58,700 


162 


1,943 


27 


11,900 


25.60 


1.86 


5,000 


1,979 


14,675 




1 


58,200 


170 


2,113 


28 


11,400 


27.53 


1.93 














57,700 


178 


2,291 


29 


10,900 


29.53 


2.00 














57,200 


186 


2,477 


30 


10,400 


31.60 


2.07 














56,700 


194 


2,671 



somehow acquired a velocity of 30 miles per hour, the 
tractive power of that engine at that velocity is 10,400 
pounds. Assume that it then strikes a +0.4% grade. 
The tractive resistance per rating ton is 8.0 +2.6, or 10.6 
pounds per ton. The tractive force required is therefore 
28,200 pounds. The deficit at this velocity is 17,800 
pounds, which must be considered as a retarding force. 



MOMENTUM GRADES. 219 

As before, since the difference of velocity heads for 29 and 
30 miles per hour equals 2.07 feet, the distance 

5^320000 

This gives the point on the +0.4% retardation curve in 
the ordinate over 29 miles per hour. The numerical work 
of computing all of these values for one curve can best 
be accomplished by a series of three columns, such as col- 
umns 5, 6, and 7 in Table XXII, following the preliminary 
set of columns from 1 to 4. Each retardation curve will 
require a similar set of columns. Figs. 27, 28, and 29 are 
copies of the diagrams prepared by Mr. A. C. Dennis in 
illustrating the article above referred to. It will be found 
that the distances given in columns 7, 10, and 13 of Table 
XXII agree substantially with the value of the ordinates 
given in these diagrams. Such discrepancies as do exist 
are due to the fact that the tractive power of the engine 
has been measured to scale from the diagram Fig. 26, 
which indicates the tractive power. 

133. Practical utilization of these diagrams. — Borrow- 
ing the example given by Mr. Dennis, assume that our 
locomotive has been loaded with 2452 rating tons behind 
the engine, which is the requirement for a +0.4% grade at 
7 miles per hour. Suppose that a start has been made 
on a level grade 5000 feet long, followed by 4000 feet of 
6.0% grade, followed by 3000 feet of -0.2% grade. Since 
the train starts on a level and is loaded on the basis of a 
+0.4% grade, we must follow its course for 5000 feet on 
the acceleration curve marked ^' level " in the diagram 
of Fig. 27. This curve has an ordinate corresponding to 
5000 feet when the train is moving at a velocity of 20 
miles per hour. This is therefore the velocity of the train 
when it strikes the +0.6% grade. The course of the 



}88j ni aomni^iQ 




^89 J ni aoTiRi&id 



MOMENTUM GRADES. 221 

train must then be studied from the retardation curve for 
0.6%. This curve has an ordinate of 3600 on the 20 
miles per hour hne. Incidentally we may remark that if 
this train had started from any point with a velocity of 
30 miles per hour up this grade, its velocity would have 
dropped to 20 miles per hour in 3600 feet. 4000 feet 
further gives us 7600 feet. The point on this curve which 
has an ordinate of 7600 feet occurs at about 8 miles per 
hour. The train then passes the summit at this velocity 
and starts on a —0.2% grade, which will evidently be an 
acceleration curve. Eight miles per hour on this grade 
corresponds to about 400 feet. Adding 3000 we have 
3400 feet, which on this curve corresponds to a velocity of 
nearly 21 J miles per hour. 

The only apparent difficulty in the above demonstra- 
tion is the fact that, when the train is starting, the resist- 
ance is far higher than the resistance which has been 
found to be so uniform at velocities above 7 miles per 
hour. Whether this would be compensated by the fact 
that at very slow velocities the tractive force may be 
largely increased by the use of sand is not very certain. 
Mr. Dennis's diagram showing the tractive force at veloci- 
ties but little above zero do not show any marked increase 
in the tractive force at very low velocities. The above 
method cannot be considered as precise, except on the 
basis that at very low velocities the resistance is no greater 
than at somewhat higher velocities, which is certainly not 
the case. These diagrams are probably very reliable for 
variations of freight-train velocities between 7 and 30 
miles per hour. They are useful in obtaining the bdiavior 
of a train through a sag or over a hump. They are prob- 
ably not so reliable when considering the movement of a 
train which starts from rest. In the numerical case just 
considered the velocity of the train at the end of the le^^e] 
grade of 5000 feet would probably be less than 20 miles 



8 8 8 




faejl m aouBjsici 



MOMENTUM GRADES. 223 

per hour, since the resistance at starting would be con- 
siderably greater. If, however, it had somehow acquired 
that velocity of 20 miles per hour at the beginning of the 
+0.6% grade, its behavior over that grade and down the 
following grade would certainly be about as computed. 

134. Another tonnage -rating formula (Henderson). — 
The following formula has been proposed by Mr. G. R. 
Henderson, and has the merit of great simplicity com- 
bined with practical agreement with the more complicated 
formulae based on elaborate tests. 

Let R = the resistance of the train or the pull at the 

tender draw-bar in pounds; 
T = the number of tons back of the tender, including 

cars and contents; 
C = the number of cars in the train; 
P = rate of grade in per cent. 

For speeds up to 12 miles per hour 

i^ = r(3.5+20P)+50C. 

Applying this formula to a numerical case, let us assume 
three trains, one a train of empties, the second half filled, 
and the third of full cars, a full load being assumed as 
twice the weight of the car. The first train has 45 empties, 
each weighing 20 tons; the second train has 28 cars, each 
weighing 20 tons and carrying 20 tons of freight; the 
third train has 20 cars, each weighing 20 tons and carrying 
40 tons of freight. Then the draw-bar pulls on a level 
would be as follows: 

R= (900X3.5) +(50X45) =5400, 
P = (1120X3.5)+(50X28)=5320, 
R = (1200 X 3.5) + (50 X 20) = 5200. 



224 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

The resistances per ton are 6, 4.75, and 4.33 respect- 
ively. 

It may be noted that the above values per ton 
are not as high for empty cars as those given by Mr. 
Dennis's tests, although the values for loaded cars 
agree fairly well. 



PART III. 

PHYSICAL ELEMENTS OF THE PROBLEM, 



CHAPTER XII. 

DISTANCE. 

135. Relation of distance to rates and expenses. — Rates 
are. usually based on distance traveled, on the apparent 
hypotheses that each additional mile of distance adds its 
proportional amount not only to the service rendered but 
also to the expense of rendering it. Neither hypothesis is 
true. The value of the service of transporting a passenger 
or a ton of freight from ^ to 5 is a more or less uncertain 
gross amount, depending on the necessities of the case and 
independent of the exact distance. Except for that very 
small part of passenger traffic which is undertaken for the 
mere pleasure of traveling, the general object to be at- 
tained in either passenger or freight traffic is the trans- 
portation from A to B, however it is attained. A mile 
greater distance does not improve the service rendered; 
in fact it consumes valuable time of the passengers and 
delays and perhaps deteriorates the freight. From the 
standpoint of service rendered, the railroad which adopts 
a more costly construction, and thereby saves a mile or 
more in the route between two places, is thereby fairly 
entitled to additional compensation rather than have it 
cut down, as it would be by a strict mileage-rate. The 

225 



226 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

actual value to a passenger of being transported from New 
York to Philadelphia depends on his individual require- 
ments, which may vary from a mere whim to the most 
imperative necessity. In one case the money value 
approaches zero; at the other extreme, money could hardly 
measure the loss if the trip were impossible. If the pas- 
senger charge between New York and Philadelphia were 
raised to $5, $10, or even $20, there would still be some 
passengers who would pay it and go, because to them it 
w^ould be worth $5, $10, or $20, or even more. Therefore, 
when they pay $2.50 they are not necessarily paying what 
the service is worth to them. The service rendered can- 
not therefore be made a measure of the charge, nor is the 
service rendered proportional to the miles of distance. 

The idea that the cost of transportation is proportional 
to the distance is much more prevalent and is in some 
respects more justifiable^ but it is still far from true. This 
is especially true of passenger service. The extra cost of 
transporting a single passenger is but little more than the 
cost of printing his ticket. Once aboard the train, it 
makes but little difference to the railroad whether he 
travels one mile or a hundred. Of course there are cer- 
tain very large expenses due to the passenger traffic which 
must be paid for by a tariff which is rightfully demanded, 
but such expenses have but little relation to the cost of 
an additional mile or so of distance inserted between 
stations. The same is true to a slightly less degree of the 
freight traffic. As shown later, the items of expense in 
the total cost of a train-mile, which are directly affected 
by a small increase in distance, are but a small proportion 
of the total cost. 

136. The conditions other than distance that affect the 
cost; reasons why rates are usually based on distance. 
— Curvature and minor grades have a considerable influ- 
ence on the cost of transportation, as will be shown in 



DISTANCE. 227 

detail in the succeeding chapters, but they are never con- 
sidered in making rates. Ruling grades have a very 
large influence on the cost, but they are likewise disre- 
garded in making rates. An accurate measure of the 
effect of these elements is difficult and complicated, and 
would not be appreciated by the general public. Mere 
distance is easily calculated; and the railroads therefore 
adopt a tariff which pays expenses and profits, even 
though the charges are not in accordance with the expenses 
or the service rendered. 

An addition to the length of the line may (and generally 
does) involve curvature and grade as well as added dis- 
tance. In this chapter is considered merely the effect of 
the added distance. The effect of grade and curvature 
must be considered separately, according to the methods 
outlined in succeeding chapters. The additional length 
considered is likewise assumed not to affect the business 
done nor the number of stations, but that it is a mere 
addition to length of track. 

137. Variable effect on expenses of extent of change in 
distance. — It will be developed later that the actual added 
expense of increasing the length of the line will depend 
very largely on the amount of that increase. An engineer 
frequently has occasion to make a slight change in the 
alinement which may make a difference in the length of 
the line at that place of a very few feet. It is demon- 
strable that certain items in the expense of operation will 
be absolutely unaffected by such a change, while other 
expenses will be increased nearly, if not quite, in their 
full proportion. On the other hand, if the change of Hne 
amounts to several miles, a very much larger proportion 
of the expenses will be increased in their full proportion. 
If the question of substituting an entirely different loca- 
tion on a division of approximately 100 miles was being 
considered, then, so far as distance itself was concerned 



228 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

(ignoring for the moment the question of curvature, 
grades, etc., which must be considered separately), the 
expenses of transporting freight over either of those two 
lines would be more nearly proportional to the exact mile- 
age. This phase of the question will be considered in 
detail later on. 

Effect of Distance on Operating Expenses. 

138. Effect of changes in distance on maintenance of 
way. — The items of maintenance of way are more nearly 
affected in proportion to the distance than any other 
group of items. In fact it will be easier to note the 
exceptions or to estimate the discount from 100%, which 
should be estimated as the additional charge for each 
subitem. The cost of track-labor, which is such a large 
percentage of the total cost of Item 1 (see Table IX in 
Chapter VI), and even of the whole group of maintenance- 
of-way expenses, will vary almost exactly in accordance 
with the distance. If the track-labor was so perfectly 
organized that there were no more laborers than could 
precisely accomplish the necessary work, working full 
time, then any additional labor would necessarily require 
a greater expenditure for laborers. Although a division 
of a road is divided into sections of such a length that a 
gang of say six or seven men will be em.ployed as steadily 
as possible in maintaining the track in proper condition, 
the addition of a few feet of track would not probably 
have the effect of increasing the number of sections, nor 
would it even require the addition of another man to the 
track-gang. It might require a httle harder work in 
maintaining a section, it might even mean a slight lowering 
in the standard of work done in order that the whole sec- 
tion should be covered. The fact remains that the cost of 
track-labor will not inevitably and necessarily be increased 
in a strict proportion to the increase in distance. On the 



DISTANCE 229 

other hand, it would not be wise to rely on any definite 
reduction or discount from the full 100% of work required, 
since to do so implies that, with the lessened distance, 
there would be some loafing on the part of the track-gang, 
or that with the added distance the men would be over- 
worked or would be compelled to slight their work. There- 
fore it is only safe to allow the full 100% addition for Item 
1, repairs of roadway. 

The items, renewals of rails and renewals of ties, should 
certainly be considered as changing in direct proportion 
to the distance. The repairs and renewals of bridges, cul- 
verts, fences, road crossings, signs, cattle-guards, . build- 
ings and fixtures, and docks and wharves (Items 4 to 7), 
may perhaps be considered in the same way, although 
there are some of these items on which the effect is more 
doubtful. If a proposed change in line does not involve 
any difference in the number of streams crossed, then the 
number of the bridges and culverts will not be altered, 
and although the size may be altered, the effect of 
the change on the cost for repairs will probably be too 
insignificant for notice. For small changes of distance it 
may very readily happen that no bridge or culvert is 
involved. For great changes of distance, especially those 
which would involve an entire change of route for a dis- 
tance of many miles, it might be proper to consider 
Item 4 to be affected fully 100%. Although Item 4 
is small, averaging about 2.5%, the error involved in 
this item by considering that the change amounts to 
100% for great distances and zero for small chstances 
will be almost inappreciable. For Item 5 the full 100% 
will be allowed for all changes of distance, for the same 
reason as previously given for repairs of roadway. Item 
6 will usually be absolutely unaffected by a small 
change in distance, since it does not usually involve any 
buildings or fixtures. Larger changes of distance will 



230 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

probably require some change in the number of minor 
buildings required, but such buildings will be the more 
insignificant buildings, and we are therefore making ample 
allowance, if, under ordinary conditions, we estimate that 
20% of the average cost of all buildings (which include 
terminals, etc.) is allowed for this item. Under ordinary 
conditions Item 7 will be absolutely unaffected by any 
changes in alinement which the engineer may make. An 
addition to distance will not usually affect the telegraph 
system, except as it adds to the number of telegraph-poles 
and to the amount of wiring and pole fixtures. Therefore 
any addition to distance will not add more than 50% to 
the average cost of this item. Items 9 and 10 are insig- 
nificant in amount, and can hardly be said to be affected 
by any small difference in distance which would ordinarily 
be measured in feet. Larger differences, which are meas- 
ured in miles and which may involve, for instance, all the 
blank forms required for the reports of an additional sec- 
tion-gang, additional pay-rolls, etc., will be increased to 
practically their full proportion. Therefore there is but 
little error involved in allowing 100% on these items for 
changes of distance measured in miles. 

139. Effect on maintenance of equipment. — The rela- 
tion between an increase in length of line and the expenses 
of Items 11, 17, 18, and 19 are quite indefinite. In some 
respects they would be unaffected by slight changes of 
distance, and yet it is difficult to prove that the expenses 
should not be considered proportionate for the distance. 
For example, the added train-mileage will increase repairs 
of rolling-stock, and will therefore hasten the deterioration 
and increase the cost of ''repairs and renewals of shop 
machinery and tools " (Item 17)o Fortunately, all these 
items are so small, even in the aggregate, that little error 
will be involved, whatever decision is made. It will there- 
fore be assumed that these items are affected 100% for 



DISTANCE. 231 

large additions in distance and 50% for small additions. 
Item 16 is evidently unaffected by any change of distance. 
Items 12, 13, 14, and 15 are therefore the only items 
which remain to be discussed, but their determination 
requires very careful computation. 

These four items constitute the repairs of the rolling- 
stock of the road. The deterioration of rolling-stocky 
which requires its repair and finally its ultimate abandon- 
ment and therefore renewal, is caused by a combination of 
a large number of causes, of which the mere distance they 
travel on the road is but one cause. They deteriorate first 
with age; second, on account of the strains due to stop- 
ping and starting; third, on account of the strains and 
wear of wheels due to curved track; fourth, on account 
of the additional stresses due to grade and change of 
grade, and fifth, ona ccount of the work of pulling on a 
straight level track. In addition to this, locomotives 
suffer considerable deterioration due to expansion and 
contraction, especially of the fire-box when the fires are 
drawn and the fire-box and boiler become cold, and again 
when the fire is started up. A large part of the expenses 
of maintaining passenger-cars is the expense of painting, 
which is a matter of mere time. Considering that the 
changes of distance, whose economic value the engineer 
tries to compute, will never make a difference in the number 
of round trips the engine or car would make in a day or 
month, the added distance which may be traveled does 
not add to the exposure of the car to the weather. There- 
fore, whatever deterioration of the car paint is due to 
weather, it will be incurred regardless of whether the length 
of the division of the road is 100 miles or 99 or 101. That 
element of the cost of car maintenance is absolutely inde- 
pendent of the precise length of that division of the road. 
On the other hand, the wear of car- and engine- wheels, 
although largely affected by curvature, is certainly affected 



232 THE JECONOMIC OF RAILROAD CONSTRUCTION. 

to some extent by wear on a straight tangent. To deter- 
mine the proportion of total wear due to these various 
causes is a matter of estimation and judgment. An 
approach to accuracy may be made by a compilation of 
the shop records of rolling-stock, repairs, showing the 
amount which is spent in various kinds of repairs, and 
estimating as closely as possible what is the cause of each 
form of deterioration. A check on any such estimate is 
the consideration that the total deterioration is simply 
the summation of the deterioration due to all causes com- 
bined. It is therefore a question of dividing 100% into 
as many portions as there are contributing causes, and to 
assign to each cause its relative importance in per cent, 
so that the sum total shall reach 100. A. M. Wellington, 

Table XXIII. — Distribution op the Cost of Engine Repairs to 
ITS Various Contributing Causes. (Copied from Wellington.) 



Item. 



Total 
cost of 
item. 



2 X « 

O cj © 
<*: btio (jj 



Distribution. 



i aw 









.-^c 



.2 5" 
^ '^ ^ 



73 -kS 

f3 fl 
03 o"e3 

5 mg So 






m 



Boiler 

Running gear 

Machinery 

Mountings 

Lagging and painting. 

Smoke-box, etc 

Tender: 

Running gear 

Body and tank 



20.0 
20.0 
30.0 



7. 

7. 

14. 



12.0 
5.0 

10.0 
3.0 



Total. 



100.0 



15. 



17, 



19. 



42. 



in his ''Economic Theory of Railway Location," dis- 
tributed the cost of engine repairs to its various contribut- 
ing causes, as shown in the following tabular form. Ho 



DISTANCE. 233 

did not claim that such an estimate was accurate and 
appHcable to all cases, but he did claim that the error 
was probably not sufficient to be of importance. A com- 
parison of these percentages, with the data given by shop 
records on any particular road, would not probably show 
a very material difference, and the writer will not attempt 
to claim that any figures he might obtain will be any 
more accurate in general, although they might be more 
accurate as applied to some particular conditions. 

It may be noted from the above table that 42% of 
engine repairs has been assigned to distance on a tangent 
between stations. If the added distance does not imply 
an extra stoppage of the train, there is but little, if any, 
reason to differentiate between the effect on repairs of a 
large or small addition to distance. We will therefore 
consider Item 12 to be affected in this ratio of 42%. 

Wellington similarly distributed the cost of freight- 
car repairs to its various causes, and by a very similar 
method estimated that 36% of such repairs were due to 
distances on a tangent between stations. The consider- 
able transformation in the construction of freight-cars, 
since the time that Wellington compiled this table, has 
certainly utterly changed the absolute cost of car repairs, 
even if it has not changed the relative percentage of the 
cost of the various items. In the lack of any better 
figures this same figure will be used for Item 14. Although 
there are evidently enormous differences between Items 
14 and 15, Item 15 is so small that it is hardly worth the 
calculation of any more precise figures, and therefore the 
same ratio, 36%, will be used for Item 15. Wellington 
made no definite calculation for the itemized cost of pas- 
senger-car repairs, but contented himself with using the 
same figure as for freight-cars, 36%. Such a percentage 
is probably very much too high, since it is estimated that 
about one-half the cost of passenger-car repairs is due 



234 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

to the work of painting, inside and out, and of maintaining 
the seats and upholstery in proper condition. Such 
repairs are chiefly a function of time, and are but Httle. 
if any, dependent on mere distance between stations. It 
is therefore considered that the passenger-car repairs will 
not be affected more than 20% by any addition of distance. 

140. Effect on conducting transportation. — Item 20, 
superintendence; Items 30 and 31, station expenses; Item 
32, switching charges; Item 34, hire of equipment, and 
Items 38 to 46 will evidently be nearly, if not quite, un- 
affected. The most of them are absolutely unaffected. 

141. Item 21. Wages of engine- and roundhouse-men. — 
In a previous chapter (§ 62) the wages of enginemen and 
roundhouse-men have been discussed. It is evident that 
the wages of roundhouse-men will be totally unaffected by 
a change of distance. The proportion which the wages of 
roundhouse-men bears to the total item has fluctuated 
between large limits during the past ten years. It has 
averaged 9%. The discussion of wages showed that even 
the enginemen are rarely, although sometimes, paid on a 
strict mileage basis. They are usually paid on a trip basis, 
in accordance with which a slight change in the distance 
will not affect the classification of the trip, and therefore 
would make no difference in the wages. We will there- 
fore say that for small changes of distance, especially such 
as would be measured in feet, this item will be unaffected; 
but that for larger changes, such as would be measured in 
miles, this item will be affected by the full amount of the 
enginemen's wages, which we will put down at the average 
value of 91% of the total item. 

142. Item 22. Fuel. — A surprisingly large percentage 
of the fuel consumed is not utilized in drawing a train 
along the road. A portion of this percentage is used in 
firing-up. A portion is wasted when the engine is standing 
gtill, which is a considerable proportion of the whole time. 



DISTANCE. 235 

The policy of banking fires instead of drawing them re- 
duces the injury resulting from great fluctuations in tem- 
perature, but in a general way we may say that there is 
but little, if any, saving in fuel by banking the fires, and 
therefore we may consider that almost a fire-box full of 
coal is wasted whether the fires are banked or drawn. 
Some tests were made on the Santa Fe, in which some 
large locomotives consumed from 1200 to 1660 pounds of 
coal merely in firing-up. But even the amount of coal 
required to produce the required steam-pressure in the 
boiler from cold water does not represent the total loss. 
The train-dispatcher, in his anxiety that engines shall be 
ready when needed, will sometimes order out the loco- 
motives which remain somewhere in the yard, perhaps 
exposed to cold weather, and blow off steam for several 
hours before they make an actual start. Of course the 
amount thus attributable to firing-up is a very variable 
one, depending on the management, and therefore no pre- 
cise figures are obtainable. But it has been estimated 
that it amounts to from 5 to 10% of the total consump- 
tion. A freight- train, especially on a single-track road, will 
usually spend several hours during the day on sidings, 
and when a single-track road is being run to the limit of 
its capacity, or when the management is not good, the 
time will be still greater. It has been found that the 
amount of coal required by an engine merely to keep up 
steam will amount to from 25 to 50 pounds per hour. If^ 
in addition to this, steam escapes through the safety-valve, 
the loss is much larger. It is estimated that the amount 
lost through a 2J-inch safety-valve in one minute would 
represent the consumption of 15 pounds of coal, which 
would be sufficient to haul 100 tons on a mile of track 
with easy grades. Again we see that the amount thus 
lost is exceedingly variable and almost non-computable, 
although as a rough estimate the amount has been placed 



236 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

at from 3 to 6% of the total. Another very large sub- 
item of loss of useful energy is that occasioned by stopping 
and starting. A train running 30 miles per hour has 
enough kinetic energy to move it on a straight level track 
for more than two miles. Therefore, every time a train 
running at 30 miles per hour is stopped, enough energy is 
consumed by the brakes to run it about two miles. There 
is a double loss, not only due to the fact of the loss of 
energy, but also because the power of the locomotive has 
been consumed in operating the brakes. When the train 
is again started, this kinetic energy must be restored to 
the train in addition to the ordinary resistances which are 
even greater, on account of the greater resistance at very 
low velocities. Of course, the proportion of fuel thus con- 
sumed depends on the frequency of the stops. It was 
demonstrated by some tests on the Manhattan Elevated 
Road in New York City, where the stops average one in 
every three-eighths of a mile, that this cause alone would 
account for the consumption of nearly three-fourths of the 
fuel. On ordinary railroads the proportion, of course, 
will not be nearly so great, but there is reason to believe 
that 10 to 20% is not excessive as an average figure. The 
amount of fuel which is consumed on account of curvature 
is, of course, a function of the curvature and will vary 
with each case. The only possible basis for a calculation 
of this amount must be somewhat as follows: Since all 
of the above calculations consider the average cost of a 
train-mile throughout the country, we must consider what 
is the average amount of curvature per mile of track 
throughout the country. By estimating, as will be developed 
in the next chapter, the proportion of the fuel expenditure 
which is due to this average amount of curvature and sub- 
tracting this, as well as the other subitems enumerated 
above, from the total average cost of a train-mile, we 
would then have the desired quantity, the cost of fuel 



DISTANCE. 237 

per mile of straight level track. Although it is not easy 
to obtain reliable statistics showing the average curvature 
per mile of road throughout the United States, there is 
reason to believe that it is not far from 35° per mile. 
According to the method of calculations given in the next 
chapter, to determine the additional fuel consumed by the 
added resistance due to 35° of curvature per mile, we 
obtain the approximate value that about 4% of the fuel 
consumption will be due to this cause. To obtain an 
average figure for the resistance due to grade is perhaps 
even harder, but on the approximate basis that the average 
amount of rise and fall per mile of track is about 11 feet 
per mile, it would seem as if 25% of the consumption of 
fuel were due to grades. Sunmiarizing the above items 
we would have 

Firing 5 to 10% 

Loss by radiation, etc. .. 3 to 6% 

Stopping and starting ... 10 to 20% 

Average curvature 4 to 4% 

Average grade 25 to 25% 



47 to 65% 
Direct hauling 53 to 35% Average 44% 



100 100 



This gives, as an average figure for the increased consump- 
tion of fuel due to one additional mile of straight level 
track, 44% of the average consumption per mile. 

143. Items 23, 24, and 25. Minor engine-supplies. — 
If water is obtained from municipal supplies and paid for 
at meter rates, then the cost will be strictly according to 
the consumption which will be nearly according to the 
number of engine-miles. Almost the only waste would 



238 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

be that occasioned by blowing off steam. Under such 
circumstances the increase in this item would be very 
nearly 100%, but, on the other hand, where the supply is 
obtained from the company's own plant, there is hardly 
any appreciable increase in expense due to the extra 
draft on the tanks. Of course the cost of pumping would 
be somewhat affected. Considering that the sum of Items 
23, 24, and 25 are only 1.26%, very little error would be 
involved if we consider as an average figure that this item 
will l)e increased 50% by any addition to distance. 

144. Item 26 includes the wages of trainmen other than 
enginemen. Their wages are paid on very much the 
same basis as the enginemen, which means usually that 
small additions of distance will not affect their wages. 
Large additions will affect them 100%. 

145. Item 27. Train-supplies and expenses include a 
very large matter of small subitems, the consumption of 
which is partly a matter of mere time and partly a matter 
of mileage. It is sufficiently precise in this case to say 
that 50% of these subitems will be affected directly as 
the mileage. 

146. Item 28. Switchmen, flagmen, and watchmen. — 
The necessity for flagmen and switchmen may be said in 
general to increase with the mileage, although it might 
readily happen that a given change in distance which is 
under consideration might not effect the slightest change 
in this item. It is quite unlikely that the number of 
switchmen would be affected. It is probable that 25% 
of this item is sufficient as an average figure. 

147. Item 29. Telegraph expenses include the wages of 
operators at stations (which are unaffected) and the special 
expenses due to offices and telegraph stations and to- 
operating the line, the maintenance of the line being 
charged to Item 8. Although it will theoretically require 
more battery material to transmit telegrams over a longer 



DISTANCE. 



239 



line, the added expense is so very slight that it may be 
utterly ignored. 

148. Item 33. Car-mileage. — As before stated, car- 
mileage is now largely paid for on the per-diem basis, 



Table XXIV. — Effect on Operating Expenses of Great and 
Small Changes in Distance. 







Per cent 


Cost per 






Per 


cent 


Cosl 


. Der 


a 




affected. 


mile. 


a 




affected. 


mile. 


fv 


Normal 
average. 








^ 


Normal 
average. 










d 


1 


'3 


i 


■^ 


,0 


1 




1 


'& 


iz; 







M 





CQ 


'A 







M 





m 
















22.906 






13.89 


5.15 


*1 


10.767 


100 


100 


10.77 


10.77 


26 


7.288 


100 





7.29 





2 


1.422 


100 


100 


1.42 


1.42 


27 


1.519 


50 


50 


.76 


.76 


3 


2.948 


100 


100 


2.95 


2.95 


28 


4 110 


25 


25 


1.03 


1.03 


4 


2.461 


100 





2.46 





29 


1.875 














5 


.542 


100 


100 


.54 


.54 


30 


7.310 














6 


2.151 


20 





.43 





31 


.728 














7 


.249 














32 


.319 














8 


.150 


50 


50 


.07 


.07 


33 


1.829 














9 


.029 


100 





.03 





34 


.287 














10 


.315 


100 





.31 





35 


.863 


100 


100 


.86 


.86 














36 
37 


.959 
.179 


100 
100 


100 
100 


.96 
.18 


.96 
.18 




21.034 






18.98 


15.75 














38 
39 


.846 
.429 


1 








11 


.617 


100 


50 


.62 


.31 








12 


6.538 


42 


42 


2.75 


2.75 


40 


1.609 










13 


2.174 


20 


20 


.43 


.43 


41 


.128 


[0 








14 


7.160 


36 


36 


2.58 


2.58 


42 


.112 











15 


.198 


36 


36 


.07 


.07 


43 


1.723 










16 


.207 














44 


.460 










17 


.570 


100 


50 


.57 


.28 


45 


.624 










18 


.042 


100 


50 


.04 


.02 


46 


.533 


1 








19 


.518 


100 


50 


"^9 


26 




















56.636 






24.97 


8.94 




18.024 






7.58 


6.70 


47 

48 




.... 








1 










20 


1.757 






















21 


9.607 


91 





8.74 





49 












22 


10.316 


44 


44 


4.54 


4.54 


50 


[ 4.306 














23 


.647 


50 


50 


.32 


.32 


51 


1 










24 


.377 


50 


50 


.19 


.19 


52 












25 


.202 


50 


50 


.10 


.10 


53 














22.906 






13.89 


5.15 


100.000 






51.53 


31 39 















* For the significance of the items, see Table IX, 



240 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

although it is sometimes paid for on a combined mileage 
and per-diem basis. On the strict per-diem basis an 
addition of a few hundred feet or even several miles would 
have no effect. On a strict mileage basis the item would 
be affected in proportion to the distance. Considering the 
very extensive adoption of the per-diem system, it is prob- 
ably nearer to the truth to consider that the item is prac- 
tically independent of distance, and therefore it will be 
here ignored, although there are cases where it should be 
included to its full value. 

149. Items 35, 36, and 37. Expenses and damage, 
although fortuitous and not items that can be definitely 
calculated or predicted, should nevertheless be allowed for 
their full value for any added distance. 

The general expenses. Items 47 to 53, will be unaffected. 

150. Estimate of total effect on expenses of small changes 
in distance (measured in feet) ; also estimate for distances 
measured in miles. — Collecting the above percentages for 
the various items we have Table XXIV, which shows that 
the average cost of operating a small additional distance 
will be about 31.39% of the average cost per unit distance. 
If the additional distance amounts to several miles, the 
added cost will amount to about 51.53% of the unit cost. 
These figures may also be considered as the saving in 
operating expenses resulting from a shortening of the line, 
and thus gives a measure of the operating value of reducing 
the length of the line. The average cost of a train-mile 
from 1890 to 1904 varied between 91.829 c. in 1895 to 
131.375 c. in 1904. The cost has been rising steadily since 
1897. Whether the cost will continue to rise or whether 
it will recede during the next few years is of course a 
matter of pure conjecture. There are many reasons to 
believe that the cost will recede somewhat from the high 
value of recent years, although it may never again sink 
to the low value of 1895, If we adopt the round number 



DISTANCE. 241 

of $1.30 as the probable cost of a train-mile during the 
next few years, we can reduce the above percentages to 
cents per train-mile, which will come to 41 and 67 c. 
per train-mile respectively. Some trains run 365 days per 
year; others run but 313 days. The tendency, however, 
is toward the larger figure, especially in the case of freight 
service, which comprises about 55% of the number of 
train-miles. The added cost per daily train per year for 
each foot of distance would therefore be 

41><365X2_ 

5280 ~^'^^ ""' 

When the distance is measured in miles the added cost 
per daily train per year for each mile of distance w^ould be 

67X365X2 = 1489. 

Of course, if such calculations are made for a light traffic 
road which only runs trains on week-days, we should use 
313 in the above equations instead of 365. It should be 
noted that the subitems in the above table which are the 
most uncertain are those w^hose absolute value is the 
smallest, and that even if we make very large variations 
in the most uncertain items, the final result will not be 
very materially altered. On the other hand, the very 
largest items are those which are capable of fairty precise 
calculations. The numerical illustration of the capitalized 
value of saving distance will be given later, see § 177. 



Effect of Distance on Receipts. 

151. Classification of traffic. — Although there are num- 
erous methods of classifying traffic, the best classification 
for the purpose of this discussion is to divide all traffic into 



242 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

two general divisions, through traffic and local traffic, the 
through traffic being here considered to mean traffic which 
passes over two or more roads, even though the total haul 
may be less than 100 miles. On the other hand, local 
traffic is here considered to mean traffic that is entirely 
confined to one road, even though it travels from one end 
of the system to the other. The following discussion will 
require a subdivision of this classification into five classes : 

(a) Non-competitive local — on one road with no choice 
of routes. 

(h) Non-competitive through — on two or more roads, 
but with no choice. 

(c) Competitive local — a choice of two or more routes, 
but the entire haul may be on the home road. 

(d) Competitive through — direct competition between 
two or more routes, each passing over two or more lines. 

(e) Semi-competitive through^a non-competitive haul 
on the home road and a competitive haul on foreign roads. 

It will be found that any other possible combination of 
conditions may be placed under one of the above five 
classes, so far as its essential effect on receipts is concerned. 
In this discussion the term "home road " applies to the 
road with whose finances we are directly concerned. The 
term "foreign road " applies to any other road with which 
traffic is exchanged, and which may or may not suffer 
loss through any change of policy on the home road. 

152. Method of division of through rates between the 
roads on which through traffic is carried. — In theory 
through rates are divided between the roads run over 
in proportion to the mileage. Frequently there is an 
arbitrary deduction made from the gross amount received 
to pay for "terminal charges " before the division is made. 
It sometimes happens that a road has sufficient financial 
strength in its dealings with other roads to demand and 
obtain the concession of a "constructive mileage," which 



DISTANCE. 243 

is in excess of the actual mileage. For instance, the rail- 
road may have been running for many years with a certain 
mileage between termini. Then a cut-ofT is made by 
means of a tunnel or some other very expensive construc- 
tion, and there may be an actual saving of several miles 
in the length of the road. If the road is financially strong, 
it may succeed in obtaining the concession of dividing the 
freight receipts according to the old system rather than 
to submit to the reduction on account of the improvement. 
Nevertheless the fact remains that receipts are supposed 
to be divided according to the relative mileage. The 
words ^ through rate" in the following discussion refer 
to the amount actually divided after preliminary deduc- 
tions have been made. Our discussion must therefore be 
based on that method, and any variations from it must 
be considered as exceptions. On account of this method 
of division and on account of the fact that non-competi- 
tive rates are almost invariably fixed according to the 
mileage, there results the unusual feature that, unlike 
curvature and grade, there is a compensating advantage 
in increased distance, which applies to all of the above 
classes of traffic except one (c — competitive local), and 
that the compensation is sometimes sufficient to make the 
added distance an actual source of profit. It has just 
been proved that the cost of hauling a train an additional 
mile is only from 31 to 51% of the average cost. There- 
fore in all non-competitive business (local and through) 
where the rate is according to the distance, there is an 
actual profit in all such added distance. In competitive 
local business, in which the rate is fixed by competition 
and has practically no relation to distance, any additional 
distance is but dead loss without any compensation. In 
competitive through business the condition of profit or 
loss will depend on the ratio of the length of the home 
haul to that of the foreign haul. The effect of this ratio 



244 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

and the law under which it works may best be illustrated 
by numerical examples. 

153. Effect of a change in the length of the home road 
on its receipts from through-competitive traffic. — Suppose 
that the home road is 100 miles long and the foreign road 
is 150 miles long. Then the home road will receive 

Y^TT— — ^ = 40% of the through rate. Suppose that the 

home road is lengthened five miles. Under this condition 

105 
it will receive -.^- -. ^^ = 41.176% of the through rate. 

The traffic being competitive, the rate will be a fixed quan- 
tity regardless of this change of distance. To simplify the 
numerical work we will consider how much the home road 
will receive on a total freight charge, which, on account 
of the competition, is fixed at $1. By the first plan the 
home road will receive 40 c. and therefore handles that 
consignment of freight at the rate of .4 c. per mile. When 
the distance is increased to 105 miles it receives for the 
handling of that consignment of freight 41.176 c. Instead 
of computing the average rate per mile, we will consider 
it as. though it received the same rate for the original 
hundred miles, and that it received 1.176 c. for the addi- 
tional five miles, or at the rate of .235 c. per mile; but 
this is at the rate of 59% of the original rate per mile. 
We have determined above that the cost per train for an 
additional mile averages about 51.5% of the average cost 
of a mile, and therefore it may be seen that the net effect 
of adding that five miles is to leave to the original 100 
miles the full rate of profit, and also that the amount 
received for the additional five miles will more than pay 
the cost of it, even though the additional profit is small. 
On the other hand, if the line is shortened five miles it 
may be similarly shown that not only are the receipts les- 
sened in gross amount, but that the saving in operating 



five miles, then it will receive ^^7^^-^^ = 80.392% of the 



DISTANCE. 245 

expenses by the shorter distance is less than the reduction 
in receipts. 

This line of argument was used by the manager of a 
railroad in opposing the plan of the directors to shorten a 
road by means of an expensive tunnel. He argued that 
under their traffic agreements the receipts of the road 
would not only be less, but also that the resultant saving 
in operating expenses would not equal the reduction in 
receipts. 

154. A second example will be considered to illustrate 
another phase. Suppose that the haul on the home road 
is 200 miles and that on the foreign road is 50 miles. In 

this case the home road will receive ^^^ -^ = 80% of the 

through rate. Suppose that the home road is lengthened 

205 
205+50 

through rate. Assuming as before that the total pay- 
ment on a given shipment of freight is $1, the home road 
will receive by the first plan 80 c, or at the rate of .4 c. 
per mile. Adding five miles, the home road will receive 
only .392 c. in addition, which will be at the rate of .0784 c. 
per mile for the additional five miles. This is only 19.6% 
of the original rate, and is but little over one-third of 
what the additional distance will actually cost. In such 
a case, although there is some compensation for the addi- 
tional distance, it is not sufficient to pay for the added 
cost. A study of the two numerical problems given above 
will show that there is some proportion of home haul to 
foreign haul at which the added receipts will just equal 
the added cost. When the home haul is a very large pro- 
portion of the total haul there is a loss, although not a 
total loss. When the haul is entirely on the home road, 
which is the case of competitive local traffic, the added 
distance is a complete loss without any compensation. 



246 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

When the added distance is a large part of the home 
haul and the foreign haul is very large, then the profit 
of the home road is considerable and the total transaction 
is distinctly profitable. A further development of this 
course of reasoning might be an interesting mathematical 
study, but its precise application is useless for the reason 
given below. 

155. Application of the above principle. — Every station 
on the home road has at least potential traffic relations 
with every other station on every other road in the coun- 
try. The traffic between each station and every other 
station presents a new combination. The effect of an 
increase of distance on one branch of the traffic will be 
more or less compensated by an opposite effect on the 
traffic between two other stations. The net effect on the 
total receipts of the road could only be obtained by the 
solution of a problem with a very large number of elements 
which are not even constant, but which are subject to 
unforeseen changes. Therefore the only practical use that 
we can make of a demonstration like the above is to derive 
from them certain general conclusions as follows. 

156. General conclusions regarding a change in distance. — 
(a) In all non-competitive business (local and through) 
the added distance is actually profitable. On some small 
roads practically all of the business is non-competitive. 
A considerable proportion of it is always non-competitive. 

(h) When the competitive local business is very large 
and the competitive through business has a large average 
home haul compared with the foreign haul, the added dis- 
tance is a source of loss. Such conditions apply almost 
exclusively to trunk lines and to competitive lines between 
large cities. 

(c) The above conclusions may be still further con- 
densed to the general conclusion that there is always some 
compensation for the added cost of operating an added 



DISTANCE. 247 

length of line, and that it may sometimes be a source of 
profit. 

(d) There is a danger in the application of the above 
argument which should not be forgotten. The argument 
might be carried to the logical conclusion that if added 
distance is profitable the engineer would be justified in 
purposely lengthening the line. But added distance means 
adding operating expenses. The increased tariff to meet 
these is a tax on the conmiunity, a tax which more or 
less discourages traffic. It is not only contrary to public 
policy but contrary to the ultimate best interests of the 
road to burden an enterprise with avoidable expenses. The 
locating engineer frequently has to choose between two 
locations, one of which saves distance by very expensive 
construction, such as deep cutting, high embankments, a 
tunnel or a bridge, while a longer line may be constructed 
at considerably less total expense, because it is almost a 
surface line. In such a situation the engineer should con- 
sider that if the bulk of the business of his road will be 
^'non-competitive local," he would hardly be justified in 
increasing the cost and thereby actually reducing the mile- 
age and the gross receipts of his road. On the other 
hand, if the road is a very important line, on which 
the bulk of the business is apt to be '^ competitive through " 
business, the added distance would probably be operated 
at a considerable loss, and therefore should be avoided 
even at a considerable added expenditure. 

(e) Finally, although there is a considerable and un- 
compensated loss resulting from curvature and grade 
which will justify a considerable expenditure to avoid 
them, there is by no means as much justification to incur 
additional expenditure to avoid distance. Of course, need- 
less lengthening should be avoided as a matter of broad 
policy. A moderate expenditure to shorten the line may 
be justifiable, and its justification will increase with the 



248 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

increase in probabilities of a heavy through competitive 
traffic. A short branch line, whose business will consist 
chiefly of non-competitive local business or of through 
business, in which the proportion of foreign haul to home 
haul will be large, will receive a very considerable com- 
pensation if not actual profit on added haul, and therefore 
will not be justified in paying any great amount of money 
to reduce distance. 

157. Justification of decreasing distance to save time. 
— A little study of this question will show that the cases 
are rare where a minor change in distance will accomplish 
any material saving in the time required to make a trip. 
It will also be clear that such a saving of time will have 
no effect on freight business which is worth considering. 
The competition for passenger business between two cities 
like New York and Philadelphia, or even New York and 
Chicago, render the time element of considerable financial 
importance, but it may readily be demonstrated that the 
saving of even ten minutes on such a trip by means of a 
change of alinement, the average speed of the trains re- 
maining the same, could only be accomplished by enor- 
mous expenditure. The cases are very rare where the 
element of time as affected by reduction of distance can 
be given financial weight. 

158. Effect of change of distance on the business done. — 
All of the above calculations have assumed for simplicity 
that the business done by the road is a definite quantity 
which is unaffected by any proposed changes. A common 
defect in the location of a cross-country line, whose busi- 
ness will virtually be that of a branch to some great trunk 
line with which it may connect, even though the small 
road is an independent road, is that too much importance 
will be given to the effort to obtain ''a, short, straight 
line " rather than a line which will reach sources of traffic. 
Of course there is a danger in either extreme. A line 



DISTANCE. 249 

which zigzags across country in an effort to reach every 
possible source of traffic may be so long that the whole 
traffic is burdened with an excess haul which will literally 
discourage traffic. The number of elements entering into 
the problem is so large that it is difficult to state a general 
rule, but the following will usually be safe. Adopt a route 
of such a length that the annual traffic per mile of line 
is a maximum. We may make the rule somewhat more 
complicated and allow for the element of cost of construc- 
tion by saying— Adopt a route of such length that the 
annual traffic per mile of line divided by the average cost 
per mile is a maximum. Even the above rules take no 
account of the effect of curvature and grade, which will, 
of course, have a considerable effect on the operating 
expenses; but a road whose receipts per mile of line is 
maximum is evidently obtaining the maximum profit from 
the community, especially if the cost of construction has 
been kept so low that the profits per mile of line divided 
by the average cost is also a maximum. 

No attempt has been made to estimate the effect of a 
saving of time on the passenger business of the very few 
trunk lines on which the competition in the matter of 
speed is so great that millions are freely spent in the 
attempt to reduce it, not only by a reduction of distance 
but by the elimination of curvature and steep grades. A 
gain in traffic which is secured wholly by competition 
only holds good as long as the advantage can be main- 
tained and until a competitor will offer still greater advan- 
tages. Under these conditions any exact analysis of the 
question is practically impossible, and considering the fact 
that such a question does not apply to any appreciable 
extent to nine-tenths of the mileage of the country, it 
will not be here further considered. 



CHAPTER XIII. 



CURVATURE. 



159. General objections to curvature. — In the popular 
mind curvature is perhaps the most objectionable feature 
of railroad alinement. The popular mind readily per- 
ceives the curvature as a fact, when a grade which is more 
costly from an operating standpoint is not perceived at 
all. The objections to curvature may be analyzed and 
classified as follows : 

(1) Danger. — The added danger of collision, derailment, 
or other form of accident which is due to curvature, are 
fully realized and even exaggerated by non-technica 
people. 

(2) Effect on traffic. — A road sometimes loses passenger 
traffic on account of the apprehension of danger, or be- 
cause the curvature produces rough and unpleasant riding, 
or because it reduces somewhat the speed of trains and 
therefore the total time between termini. 

(3) Effect on operating i^rams. ^Curvature has some 
limiting effect on the length of trains, and it is claimed 
that it limits the use of heavy engines. 

(4) Effect on asperating expenses. — Curvature increases 
these expenses by increasing (a) the required tractive 
force; (5) the wear and tear of road-bed and track; (c) 
the wear and tear of equipment; and {d) the required 
number of track-walkers and watchmen. The above 
objections will be considered in order. 

250 



CURVATURE. 251 

i6o. Financial value of the danger of accident due to 
curvature. — This subject has akeady been considered in 
Chapter I, under the general subject of accidents. Special 
objection is urged against curvature, on the ground that 
it increases the danger of accidents, that accidents are 
more liable to occur on a curve than on a straight track, 
and that when they do occur the results are apt to be 
far worse than when on a tangent. The subject is some- 
times considered from the standpoint of eliminating curv- 
ature altogether, but this is usually financially if not 
physically impossible. We are chiefly concerned from a 
practical standpoint with an effort to obtain easy curva- 
ture rather than sharp curvature, or to reduce the number 
of degrees of central angle. If we study Mie statistics 
published each year regarding the total number of rail- 
road accidents in the country and attempt to estimate 
the number which happened on curves, and then attempt 
to estimate the number of those accidents which would 
have been avoided if the track had not been curved, or 
if the track had had easy curvature rather than sharp 
curvature, it will be found that the estimated number 
for which curvature, and especially sharp curvature, was 
directly responsible is very small. If we can estimate 
the number of railroad curves in the United States, the 
immense train mileage on them, and then compute the 
probabilities that an accident will happen on any one 
particular curve during any year or during a term of say 
100 years, we will find that the probabilities are exceed- 
ingly small. If we then attempt to compute, on the basis 
of these probabihties, how much money should be annually 
expended in order to avoid an accident which might prob- 
ably happen in the course of the computed term of years, 
we would find that this annual sum would be absolutely 
insignificant. In fact we are forced to the conclusion 
tliat we are not justified in spending money to reduce 



252 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

curvature on account of the danger of accident. Of 
course this does not mean that there are not special cases 
in which accident is especially liable to happen and which 
thoroughly justifies a demand of expenditure to avoid it. 
For example, a very sharp curve in a mountainous region 
may circle around the end of a steep ridge, so that the 
view of the track is obstructed and prevent the engineer 
from discovering a landslide which might fall down from 
the steep side slopes. Such a case is an example of many 
cases of special danger which justify and demand the 
employment of special watchmen and flagmen to watch 
the condition of such dangerous places in the road. But 
these are simply exceptions which have no application to 
the general rule. We may therefore dismiss this phase 
of the question. 

i6i. Effect of curvature on traffic. — It is well known 
that the sharp curvature found on some of our east and 
west lines passing over the Allegheny Mountains has some 
effect in deterring travel from those lines. Women and 
children will grow ^'car-sick " while passing around some 
of these sharp curves at a comparatively high speed. 
But, on the other hand, a road which is so located usually 
has the compensation of attractive mountain scenery 
which may attract additional travel to an extent as great, 
if not greater, than the loss due to the crooked line. Again 
it must be considered that such an objection will only 
apply to a very small proportion of the competitive pas- 
senger traffic. The great bulk of the passenger traffic is 
unaffected while the freight traffic is absolutely unaffected. 
We are therefore justified in throwing this consideration 
out of account. Analogous to the above is the objection 
that a crooked line reduces the ability to make fast time 
and may deter travel on account of the apprehension of 
danger, but we may again consider, as above stated, that 
its effect is exceedingly small, and that whether small or 



CURVATURE. , 253 

large the general character of the country will absolutely 
prevent any change of plan which will materially affect 
the road in that respect. We are therefore justified in 
eliminating this phase of objections from our financial 
calculations. 

In the chapter on Distance (§ 157) we have already 
considered the justification of a reduction of distance in 
order to save time on roads having a very large amount 
of competitive passenger traffic. On just such roads the 
reduction of even the rate of curvature assumes financial 
value. When express-trains are required to make an 
average speed, for considerable distances of more than 
60 miles per hour, the reduction of the rate of curvature 
becomes an important matter, since at such a speed the 
superelevation of the outer rail on curves of even mod- 
erate curvature becomes so high that it is objectionable, 
and the operation of such curves at high speed becomes 
dangerous. Even the nervous strain on the engineman, 
due to watching for danger when rounding a sharp curve 
at very high speed, cannot be ignored, and on this account 
many railroads will spend considerable money to increase 
the radius of curvature, even though they are unable to 
reduce the number of degrees of central angle; but all 
these considerations apply only to that very limited por- 
tion of the traflSc on a very small percentage of the total 
railroad mileage. Very few engineers ever have occasion 
to consider such cases. 

162. Effect of curvature on the operation of trains. — It 
is true that curvature does increase the resistance to 
traction and that uncompensated curvature, when located 
on a ruling grade, virtually adds to the rate of that grade, 
and therefore might have a limiting effect on the length 
of trains which would prove very serious. This, however, 
can almost always be avoided by compensation for curv- 
ature. There are a few very rare cases, of which the 



254 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

Hudson River Railroad is the most conspicuous example, 
in which the general grade of the road for many miles is 
almost level, and yet where, on account of the rocky 
bluffs on the river-bank, sharp curvature is unavoidable, 
except by enormous expenditure. In such a case curva- 
ture may actually have a limiting effect on the length of 
trains, but such an exception is so very rare that it need 
not in general be considered. 

Limiting the use of heavy engines. — It has been asserted 
that very sharp curvature will prevent the use of the 
heaviest types of engines. While such an objection will 
probably have some force, if applied to abnormally sharp 
curvature, such as 18° or 20° curves, it hardly has any 
force for curves which are even as sharp as 10° curves. 
The '^consolidation" engine was originally designed for 
use on the sharp curves and steep grades of the mountain 
division of the Lehigh Valley Railroad. It has even been 
claimed as the result of tests that the consolidation engine 
has less resistance per ton on sharp curves than an engine 
of the "American " type. Although these tests have been 
subject to question regarding their accuracy, it is quite 
evident that they were sufficiently accurate to prove that 
sharp curvature does not prevent the use of heavy engines 
or even make an abnormal reduction in their efficiency on 
sharp curves. 

We therefore reach the only rational objection to curva- 
ture which may be directly computed in dollars and cents, 
and that is the increase in operating expenses. 

Effect of Curvature on Operating Expenses. 

163. Relation of radius of curvature and of degrees of 
central angle to operating expenses. — It does not need 
proof that the sharper the curvature the greater will be 
the tractive force required. The rail wear and also the 
general wear and tear on road-bed and track per foot of 



CURVATURE. 



255 



length will also be increased. If we attempted to estab- 
lish a relation between operating expenses and the radius 
of curvature, we would also have to consider the total 
length of the curve before we could determine the true 
effect on the operating expenses of any particular curve. 
A method of calculation, which is much more simple and 
which is sufficiently accurate for the purpose, may be 
made by establishing a relation between operating expenses 
and the number of degrees of central angle in a curve. 
The outline of the method is as follows : 

(1) It has been found that if two tangents, which make 
an angle i, are connected by a curve of large radius, 
such as the curve AB, the total cost in operating expenses 




Fig. 30. 

for the curve AB will not be materially different from that 
of the track ACDB, which has the sharp curve CD. Of 
course the wear on the sharp curve CD per foot of length 
will be much greater than the wear per foot of length on 
the track AB, but, on the other hand, the reduction of 
average track expenses per foot on the straight track AC 



256 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

and DB will cause the general average for track expenses 
to remain substantially the same. Therefore we may say 
that when we are compelled to change the course of a 
line by so many degrees of central angle, it makes no 
material difference, so far as track expenses are concerned, 
whether we employ a sharp curve or an easy curve. The 
sharp curve will concentrate the increase of expenses to 
within a few feet. The easy curve will merely spread it 
over a greater distance, but the total extra cost of the 
curve will be substantially the same in either case. 

The distinction between the desirability of reducing the 
rate of curvature in order to attain high speed and the 
extra cost of operating freight-trains, and the compara- 
tively low-speed passenger-trains which comprise the 
business of perhaps 90% of our railroad mileage, must be 
here clearly appreciated. Although no accuracy is claimed 
for such a broad statement, it is much more nearly true 
than any other statement regarding curvature which has 
equal simplicity. 

(2) At what degree of curvature is the total train re- 
sistance double its value on a tangent? No one figure w^ill 
be exact for all conditions. Train resistance varies with 
the velocity and with the various conditions of train load- 
ing even on a tangent, and the ratio of train resistance on 
a curve and on a tangent varies according to the condi- 
tions. As an approximate statement, w^e may say that a 
train running at average velocity on a 10° curve will 
encounter an extra resistance due to curvature which is 
about equal to the average resistance on a level tangent. 
We can therefore make a second general statement that 
on a 10° curve the resistance will be double the resistance 
on a level tangent. 

(3) The cost of operating a train one mile is approxi- 
mately so much, say $1. If we double the tractive re- 
sistance, we will increase certain items of expenditure, 



CURVATURE. 257 

although many other items are unaffected. The combined 
value of the affected items will aggregate a certain pro- 
portion of the cost of a train-mile. A mile of continuous 
10° curve contains 528° of central angle, and on the basis 
of assumption (2) a mile of such track will double the 
tractive resistance. Therefore, each degree of central 

angle is responsible for ^^ of the extra cost of the double 

tractive resistance. Since the increase as computed is 
irrespective of the radius and depends only on the number 
of degrees of central angle, we may therefore say that 
each degree of central angle of a curve will add that com- 
puted percentage to the average operating expense of a 
train-mile. 

This percentage however is based on the extra cost of 
a curved track over a straight level track. The average 
figures which we have for the cost of a train-mile are 
based on the cost of an average mile as it actually exists, 
including all grades and curves. This cost will evidently 
be somewhat greater than the cost of operating one mile 
of straight tangent; but w^hen we consider that the average 
amount of curvature per mile of track and the average 
amount of grade per mile of track is quite small, and that 
its influence in many items in the cost of operating a train- 
mile is very small, if not zero, we can appreciate the fact 
that, while the cost of operating a mile of plain level 
track is far less than that of operating a mile of track with 
heavy grades and sharp curves, it will not be very much 
less than the cost of operating a mile of average track. 
Therefore, although we might make some allowance for 
this item, we could not allow^ very much. 

164. Effect of curvature on maintenance of way. — A 
\ery large proportion of the items of expense in a train- 
mile are absolutely unaffected b}^ curvature. It will 
therefore simplify matters somewhat if we at once throw 



258 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

out all the unaffected items. Of the items of maintenance 
of way and structures, all but the first three may be thrown 
out. Item 4 would be affected in case a bridge or a trestle 
occurred on the curve considered, but since the very large 
majority of bridges and trestles are purposely made 
straight, and that only a very minute proportion of the 
total length of the curves of a road will be found on its 
bridges and trestles, the effect of this exceedingly small 
percentage on the cost of this small item would be so very 
minute that it may be utterly neglected. 

165. Item I. Repairs of roadway. — A very large pro- 
portion of the subitems are absolutely unaffected. The 
care of embankments and slopes, the ditching, weeding, etc., 
are evidently unaffected. The track-labor on rails and 
ties and the work of surfacing will evidently be somewhat 
increased, and yet it is very seldom that the length of a 
track section would be decreased simply on account of 
excessive curvature throughout that section. We are 
here trying to estimate how much this item, which con- 
sists largely of track-labor, will be affected by 528° of 
central angle per mile. In the previous chapter an approx- 
imate estimate was made that the average curvature per 
mile of road for the whole United States is about 35°. 
528° of curvature in a mile probably does not frequently 
occur. It would mean the equivalent of nearly IJ com- 
plete circles, and yet it is probably a generous estimate 
to say that the track-labor and other expenses belonging 
to this item would not be increased more than 25% for 
such an amount of curvature. 

166. Item 2. Renewals of rails. — It has already been 
demonstrated in Chapter IX, §§ 102 and 103, that 
the rate of rail wear on curves seems to bear some rela- 
tion to the stage of that wear in the life-history of the 
rail, and also that the rail wear is nearly, if not quite, 
proportional to the degree of the curve. Since the funda- 



CURVATURE. 259 

mental feature of the method of obtaining the effect of 
curvature on the operating expenses is to assume that 
the extra expense varies as the number of degrees of 
central angle, we may here assume that the law is also 
applicable to the wear of rails. In § 103 it w^as computed 
that the excess rail wear on a 10° curve would be 326% 
of the rail wear on a tangent. Wellington assumed that 
the extra rail wear on a continuous 11° 20' curve would 
be 300%, which would be the equivalent of 268% extra 
rail wear on a 10° curve. Although the value determined 
above is considerably more than Wellington's value, it is 
based on what are perhaps the most complete and reliable 
series of tests ever made on such a subject, and we will 
therefore assume the value 326%. 

167. Item 3. Renewals of ties. — Curvature affects ties 
by increasing the rail-cutting and by requiring more 
frequent respiking, which spike-kills the ties even 
before they have decayed. Wellington estimates that a 
tie which will last nine years on a tangent will last but six 
years on a 10° curve. He adds 50% for tie renewals. 
He considers the decrease in tie life to be proportional to 
the degree of curve. This statement is again a verifica- 
tion of the general statement in § 163, that the extra cost 
per foot of the sharper curvature just balances the extra 
length of the easier curvature. 

168. Effect of curvature on maintenance of equipment. 
— ^Items 11, 16, 18, and 19 will be considered as unaffected. 
There is little if any rational cause for assigning any defi- 
nite increase in any of these items, owing to curvature of 
the track. 

169. Item 12. Repairs and renewals of locomotives. 
— Curvature affects locomotive repairs by increasing very 
largely the wear on tires and wheels, and also the wear 
and strain due to the additional power required. Since 
the resistance due to curvature is very small compared to 



260 THE ECONOMICS OF RAILROAD CONSTRUCTION". 

that due to even a moderate grade, this last cause may be 
neglected altogether. Referring to Table XXIII (§ 139)^ 
we find an estimate that 19% of the cost of engine repairs 
is assigned to curvature and grades combined. Of this 
amount two- thirds, or, say, 13%, should be assigned to 
curvature alone. On the basis that the average curvature 
of the roads of the country is about 35° per mile, which 
is about one-fifteenth of the 528° of curvature per mile 
which we are considering, then, if 35° is responsible for 
13% increase in engine repairs, 528° would be responsible 
for 196%. It must be admitted that the above computa- 
tion is grossly approximate, and that it contains the un- 
warrantable assumption that the extra cost of engine 
repairs which is due to curvature will be strictly in pro- 
portion to the degrees of curve. Although it is probably 
not true that 528° of curvature would increase the cost 
of engine repairs by 15 times the extra cost of 35° of curv- 
ature, yet it is probably true that for ordinary variations 
from that average of 35° per mile the increased cost of 
engine repairs will be approximately as the number of 
degrees of curve, and therefore our final value is not neces- 
sarily far out of the way. If 35° is responsible for an 
increase of 13%, 1° would be responsible for about .37 of 
1%. In allowing an increase of 196% for 528° we are 
also allowing .37 of 1% per degree of central angle. 

170. Items 13, 14, and 15. — By a similar course of 
reasoning to that above given, the estimates for Items 
14 and 15 will be made 100%, while that for Item 13 will 
be made only 50%, because such a large proportion of the 
expenses of Item 13 are due to painting and maintaining up- 
holstery,which have no relation to variations in aHnement. 

171. Item 17. The repairs and renewals of shop machin- 
ery and tools will not be increased more than 50% per 
mile for the additional repairs required on the above 
equipment. 



CURVATURE. 261 

172. Effect of curvature on conducting transportation. — 

An inspection of the items under this general heading 
will show us that we may at once throw out as unaffected 
all the items except those which concern engine-supplie?, 
flagmen, and watchmen, and the group which refers to 
accidents. 

173. Items 22, 23, 24, and 25. — The required quantities 
in this calculation are the additions to cost resulting from 
the introduction of 528° of central angle into a mile of 
track. We have assumed that this amount of curvature 
will exactly double the resistance. We found in Chapter 
XII (§ 142) that the average increase in fuel consumption 
due to direct hauling amounts to about 44%. We have 
here assumed that the added curvature exactly doubles 
the work. We will therefore charge 44% of the average 
cost of a train-mile for this extra curvature. Since the 
consumption of water and other engine-supplies is roughly 
proportional to the consumption of coal, there will evi- 
dently be no error worth considering in assigning this same 
percentage to Items 23, 24, and 25. 

174. Item 28. — There are many cases where a danger- 
ous curve justifies and requires the employment of a 
special watchman to give timely notice of any dangerous 
condition of the track. Such special cases would, of 
course, justify a considerable expenditure to eliminate the 
dangerous features of that particular location, but such a 
charge should not be made against curvature in general. 
Ordinarily the elimination -or retention of a curve will not 
involve the question of watchmen and flagmen in any 
way. We are therefore justified in disregarding this item 
altogether as a general proposition, if we keep in mind 
that the item should be included when we are considering 
the elimination of some particularly dangerous curve. 

175. Items 35, 36, and 37. — This group of items, which 
refer to accidents and the increased danger of accident due 



262 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

to curvature, and therefore the amount of money which 
might be justifiably spent to avoid this danger, has already 
been referred to in § 160. It was there shown that, al- 
though there might be special cases which would justify 
considerable expenditure on account of specific dangers 
in the situation, we cannot ordinarily give any definite 
financial value to this item as applied to curvature in 
general. We therefore must eliminate these items as 
affecting the cost of curvature in general. 

General expenses. — Items 47 to 53 will also be un- 
affected. 

176. Estimate of total effect per degree of central angle. 
— Compiling the above estimates we have Table XXV. 
According to the table 528° of curvature in one mile 
will increase the expenses of each train passing over 
it by 35.425% of the average cost of a train-mile, and, 
according to the general principles laid down in § 163, 
one degree of central angle of any curve, no matter what 

the radius, will increase the expenses by -r^ of 35.425%, 

or .0671% per degree. Therefore, the cost per year per 
dail}^ train each way, at the average rate of $1.30 per train- 
mile, would be 

130 X. 0671% X2X 365 = 63.68 c. 

For a round number we will call this 64 cents. 

To forestall one Kind of objection to the foregoing course 
of reasoning, it should be remembered that many of the 
estimates of additional cost, instead of being actually 
based on the effect of a continuous 10° curve, were based 
on the observed effects of lighter curvature, which were 
then multiplied by a factor to obtain the effect of a con- 
tinuous 10° curve, as if the effects of curvature were strictly 
proportional to the curvature; but since we afterward 
divide our final result by 528 to obtain the effect of one 



CURVATURE. 



263 



Table XXV. — Effect on Operating Expenses of Changes in 
Curvature. 



Item 

No. 



1 

2 

3 

4-10 



Item (abbreviated). 



Roadway 

Rails 

Ties 

Bridges, buildings, etc 

Maintenance of way 

Superintendence 

Repairs, locomotives 

Repairs, passenger-cars 

* ' freight- cars 

* ' work-cars 

Marine equipment 

Shops 

Miscellaneous 

Maintenance of equipment 

Superintendence 

Enginemen 

Fuel 

Water 

Oil, etc 

Other supplies 

Train and station service, etc. 

Conducting transportation 

General expenses 



Normal 
average. 



10.767 
1.422 
2.948 
5.897 



21.034 



Per cent 
affected. 



25 

326 

50 





Cost per 

mile, 
per cent. 



2.692 

4.636 

1.474 





8.802 



11 
12 
13 
14 
15 
16 
17 
18-19 



.617 

6.538 

2.174 

7.160 

.198 

.207 

.570 

.560 





196 

50 

100 

100 



50 





18.024 





12.814 

1.087 

7.160 

.198 



.285 





21.544 



20 
21 
22 
23 
24 
25 
26-46 



1.757 

9.607 

10.316 

.647 

.377 

.202 

33.730 





44 
44 
44 
44 




56 . 636 







4.539 

.285 

.166 

.089 





5.079 



47-53 



4.306 



100.000 



35.425 



degree of curvature, and then multiply this constant by 
the number of degrees of central angle, as found inordinary 
practice, our calculations are not thereby vitiated because 
the effect of curvature is not strictly proportional to the 
rate of curvature. It is probably true that within the 
ordinary limits of variations in rate of curvature the 
above calculations are substantially true. In extreme 
cases they are probably in error, although it is likewise 
probably true that extreme curvature will have a variable 



264 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

effect on the rate of increase of the various items, and 
that even in extreme cases the error will not be very 
large. 

177. Nxunerical illustration. — In Fig. 31 is illustrated a 
case of a crooked line from which a considerable saving of 
curvature was made, although at a very large expendi- 
ture for earthwork, by eliminating the reverse curvature 
and all that part of the direct curvature which is necessary 
to balance the reversed curvature. This change of loca- 
tion was recently made by the Pennsylvaina Railroad, 
and involved not only the elimination of some very sharp 
curves, w^hich prevented very high speed, but also elim- 
inated about 494° of curvature and incidentally reduced 
the length of line by about 4700 feet. The total number 
of degrees of central angle in the original line is approxi- 
mately 582, of which about 335° is in one direction and 
about 247° in the other. The new line therefore eliminates 
all of the curvature in one direction (247°), but likewise 
as much curvature in the other direction. 

This problem also involves the reduction in the length 
of the line by about 4700 feet. The cost of this improve- 
ment was very great, since it involved the construction of 
four new bridges crossing the Conemaugh, and also some 
very heavy earthwork, four of the cuts having a depth at the 
highest point of 80, 105, 106, and 120 feet. The improve- 
ment was also combined with the widening of the road-bed 
for four tracks instead of two. On account of the very 
large amount of through competitive traffic hauled over 
the Pennsylvania hues, this reduction in distance is of 
benefit to the railroad to its full value on such traffic. It 
is not to be supposed that this reduction of 4700 feet in 
distance has the slightest effect in reducing the revenue 
received by the road. 

In order to compute numerically the value and justifica- 
tion of the above improvement, it is necessary to know 



CURVATURE. 



265 










266 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

the number of trains actually using those tracks, and also 
the cost of the improvement. The determination of the 
number of trains is not easy, since the number of passenger- 
trains, which alone run by regular schedule, is but a small 
proportion of the total. The number of freight- trains is 
not even a constant quantity, since it varies from day 
to day with fluctuations of the traffic. The author has 
been unable to obtain any statement of the total number 
of trains on this division. Even the cost of the reduction 
of curvature and distance is so bound up with the cost of 
widening the road-bed for four tracks instead of two that 
it is impracticable to test, even by the above method, 
whether the improvements were justified. According to 
the curvature formula the saving on each regular train 
operating that stretch of track every day for one year 
would be 

494° X 64 cents = $316.16. 

The added saving per train per year on account of the 
reduction of distance would be 

4700X5.67 cents = $266.49. 

The sum of these gives $582.65, the annual saving on 
each regular daily train. To allow for fluctuations, the 
average number of trains per day should be used as a mul- 
tiplier. On the basis that this average number is 100, we 
have a computed annual saving of $58,265. Capitalized at 
5%, this indicates a justifiable expenditure of $1,165,300. 

If the original line in the above case had been con- 
structed on a uniform grade, and if that grade had been the 
ruling grade, then since the new line is considerably shorter, 
the question of the grade of the new line would have been 
a very important one. In fact the improvement would have 
lost all of its value if its accomplishment had required an 



CURVATURE. 267 

increase in the ruling grade of the road. But the new 
line has been put in with a ruling grade of 1.15% against 
east-bound traffic. Even this will doubtless be operated 
by pusher-engines for all heavy trains. 

178. Reliability and value of the above estimate. — No 
extreme accuracy is claimed for the above method of 
estimating the effect of curvature. The effect of curva- 
ture depends on so many conditions, some of which are 
variable, that an estimate which might be mathematically 
perfect at one time would be somewhat altered during the 
succeeding year, on account of a change in operating con- 
ditions. Therefore the value obtained by any such cal- 
culations must be only considered as approximate. Never- 
theless, it does give a value for the proposed change which 
is far better than a mere guess as to the desirability of an 
improvement. The real value of these figures may be 
tested as follows : If you vary some of the very important 
items very largely, it has a comparatively small influence 
on the final result. As an illustration, suppose that the 
item of renewals of rails is assumed to be affected 500% 
rather than 326%. The effect on the value of the reduc- 
tion of 1° of curvature is increased less than 7%, which 
of course means that the justifiable expenditure to effect 
this result might and would be increased by the same 
percentage, but after all the real question is not whether 
the improvement in an ordinary case is worth, say, $10,000, 
or $10,700, seven per cent more. Possibly the extra work 
may be done for $3000 or it may require $25,000. In the 
first case there is but little question that the iriiprovement 
will be justified in view of the probable growth in the 
business of the road. In the second case it would prob- 
ably show that the improvement should be delayed until 
the amount of actual traffic will furnish a better justifica- 
tion for the work. If the estimated cost of the improve- 
ment very nearly equals the computed operating value of 



268 THE ECNOOMICS OF RAILROAD CONSTRUCTION. 

the change, the final decision on the question would depend 
very largely on the financial ability of the road to make 
such an improvement. 

Compensation for Curvature. 

179. Reasons for compensation. — When curvature and 
grade are combined on a track, the effect of the curvature 
is to increase the total resistance. This increase may be 
sufficient to have a material effect on the operation of 
trains. On minor grades the added resistance is of but 
little importance, since its virtual effect is the same as 
increasing the rate of grade somewhat; and if the virtual 
rate of grade which represents the sum of the two forms 
of resistance is still within the rate of the ruling grade, 
the net effect is merely to increase a few items of expense 
as given previously in this chapter. When the actual 
grade is nearly or quite equal to the ruling grade of the 
road, then the additional resistance caused by the curve 
will be the equivalent of a grade which is perhaps higher 
than the nominal ruling grade of the road. If we assume 
that the resistance on a 6° curve is 6 pounds per ton, which 
is the equivalent of the grade resistance on a 0.3% grade, 
then if a 6° curve were located on a 1% grade the resist- 
ance of a train on that grade would be practically the 
same as the resistance of that train on a 1.3% grade with 
straight track. If 1% grades were the ruling grades of 
that line and freight-trains were made up so that their 
engines would be taxed to the limit of their capacity on 
the 1% grade, then they would probably be stalled on 
the 6° curves, since the total resistance on those curves 
would be 30% higher than on the straight track having 
a 1% grade; but if the grade over these 6% curves is cut 
down to 0.7%, then the total resistance at such a point 
would still be equal to the resistance on a 1% grade with 
straight track. This effect can be illustrated by a dia- 



CURVATURE. 269 

gram as in Fig. 32. Assume that a stretch of track con- 
sisting of alternate tangents and curves has an actual grade 
represented by the line .4A^. The angle between BN and 
BC represents the grade which is the equivalent of the 
added resistance caused by the curve BC. Then the tan- 
gent CD is drawn parallel to AN. Similarly the line DE 



C—- ^-- 






^CtUi 



.^'-j--^^:^'^^"^' 
.^-^--i^^^^- 



alS^ 



Fig. 32. — Effect of uncompensated curvature. 

makes an angle with BN equal to the equivalent grade 
resistance of the curve DE^ and the angle of DE with the 
horizontal line represents a grade on which the resistance 
would be the equivalent of the total resistance on the 
curve DE, and then we have the line EF parallel to the 
line BN . The average resistance throughout that stretch 
of track would evidently be represented by the line A.F, 
and therefore the angle FAN represents the grade which 
would cause a resistance equal to the average resistance 
actually caused by the curves. This figure therefore 
illustrates the fact that if the grade of a stretch of track, 
consisting of curves and tangents, is kept actually uniform, 
the virtual grade of that track is somewhat higher than 
the actual grade. If it becomes necessary for trains to 
stop on these curves, then the full effect of the resistance 
is encountered and the virtual grade would be as repre- 
sented by the lines BC and DE. If it is possible to operate 
the trains throughout that stretch of track without any 
stops, then the virtual grade would be reduced approxi- 
mately to the grade AF, since the trains would regain on 



270 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

the tangents a portion of the energy which was lost on the 
curves. 

If, on the other hand, the rate of grade is reduced on 
the curves, so that the actual grade is as shown by the 
line ABCDEF in Fig. 33, the reduction of the grade on 




Fig. 33. — Grade virtually uniform, with compensated curves. 

the curves being just equal to the difference of grade 
which will represent the added resistance of the curves, 
then the virtual grade of the entire stretch of line will be 
as represented by the line AG. 

In laying out a ruling grade which is to carry a line to 
a summit, the compensation for curvature must unques- 
tionably be provided, but it adds a complication which is 
also illustrated in Fig. 33. An engineer is frequently 
required to '' develop " his hne in order to have the neces- 
sary length for a given elevation to be overcome, in order 
that the grade shall be kept within some chosen limita- 
tion; but if the grades are actually reduced on the curves, 
the total horizontal distance required to overcome a ver- 
tical elevation of HG at the rate of grade shown by the 
tangent AB equals AH, but the distance actually required 
when the curves are compensated is something more, and 
is represented by the line AK in Fig. 33. The problem 
is further complicated, owing to the fact that the necessary 
additional distance can only be obtained by additional 
"development," which of itself usually implies -additional 



CURVATURE. 271 

curvature, and perhaps a great deal of it. In order to 
compensate this additional curvature there is required a 
still further increase in horizontal distance. The locating 
engineer therefore is confronted by the problem of intro- 
ducing considerable added length of track and perhaps 
considerable added curvature, in order to obtain a ruling 
grade on which the resistance is virtually constant through- 
out, whether on a tangent or on a curve, and on which 
the maximum resistance does not exceed that of the 
chosen ruling grade for the line. Nevertheless, consider- 
ing the supreme importance of avoiding an increase in the 
ruling grade (as will be developed later) and the compara- 
tive unimportance of an increase in distance or curvature, 
such a method is literally the only correct method to 
follow. 

1 80. The proper rate of compensation. — This evidently 
is the rate of grade of which the resistance just equals the 
resistance due to the curve. Unfortunately for the sim- 
plicity of our calculations curve resistance is variable. 
It is greater for very low velocities. It depends somewhat 
on the detailed construction of the rolling-stock, although 
fortunately the differences in this respect are not great. 
When starting a train the curve resistance may amount 
to two pounds per ton per degree of curve. Such a resist- 
ance is equivalent to that encountered on a 0.1% grade. 
On this account the compensaton for a curve which occurs 
at a known stopping-place for the heaviest trains should 
be 0.1% per degree of curve. On the other hand, the 
compensation required for very fast trains may be as low 
as 0.02% or 0.03% per degree of curve. But these trains 
are not the trains which are usually limited by grade. 
It is the comparatively slow and heavy freight-trains 
which must be chiefly considered in the study of ruling 
grades. Therefore from 0.04% to 0.05% must be used as 
the rate of compensation for average conditions. Even 



272 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

these figures must be considered as only applicable to the 
ordinary and usual degrees of curvature. 

It has been found that the resistance on the excessively 
sharp curvature used on street-railways or on elevated 
railroads is far less per degree of curve than the above 
figures would indicate. This is due to the fact that the 
actual resistance on a curved track is the sum of a number 
of resistances, some of which are virtually independent of 
the rate of curvature. Curves which occur immediately 
below a known stopping-place for all trains need not be 
compensated, for the extra resistance of the curve will 
reduce by that amount the work required from train- 
brakes in stopping the train. On the other hand, if a 
.curve occurs just above a stopping-place it is a serious 
matter and should be amply compensated. In either 
case the down-grade traffic is not affected and therefore 
need not be considered. Although the suggested rate of 
compensation (0.04% or 0.05%) is possibly somewhat 
excessive, it has been recommended on the general prin- 
ciple that it is preferable that the compensation should be 
somewhat ample in order that it shall be sufficient for all 
cases. It is quite possible, however, that the excessive 
rate of compensation might require a steeper grade on 
the tangents, in order that the desired summit shall be 
reached in a given horizontal distance. In such cases the 
rate of compensation should be reduced to 0.035% or 
even 0.03%. Rules for compensation may therefore be 
stated as follows : 

(1) On the upper side of a stopping-place for the heaviest 
trains compensate 0.10% per degree of curve. 

(2) On the lower side of such a stopping-place do not 
compensate at all. 

(3) Ordinarily compensate about 0.05% per degree of 
curve. 

(4) Reduce this rate to 0.04% or even 0.03% per degree 



CURVATURE 273 

of curve, if the grade on the tangents must be increased 
in order to reach the required summit. 

(5) Reduce the rate somewhat for curvature above 8° 
or 10°. 

(6) Curves on minor grades need not be compensated, 
unless the minor grade is so heavy that the added resistance 
of the curve would make the total resistance greater than 
that of the ruling grade. 

i8i. The limitations of maximixm curvature. — What is 
the maximum degree of the curvature which should be 
allowed on any road? Unquestionably there is no definite 
limit. If any limitation is made it depends on the general 
character of the country and on the amount of traffic 
which may be immediately expected. As an extreme case 
in the justifiable use of sharp curvature, we may con- 
sider a portion of the line from Denver to Leadville, Colo. 
The traffic that was expected on the line was so meager, 
and the general character of the country was so forbidding, 
that a road built according to the usual standards would 
have cost very much more than would have been justified 
by the expected traffic. The lines as adopted cost about 
$20,000 per mile, and yet in a stretch of 11.2 miles there 
are about 127 curves. One is a 25° 20' curve, 24 are 24° 
curves, 25 are 20° curves, and 72 are sharper than 10°. 
If 10° had been made the limit (a rather high limit accord- 
ing to usual ideas), it is probable that the line would have 
been found impracticable (except with prohibitive grades), 
unless four or five times as much per mile had been spent 
on it, and this would have ruined the project financially. 

As an illustration of the other extreme, we may con- 
sider some of the improvements which have been recently 
made on the P. R.R. between Philadelphia and Pittsburg. 
Millions of money have been spent in the effort to reduce 
distance, curvature, and grade. The reduction of curva- 
ture has been very largely in the form of eliminating 



274 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

degrees of central angle, but it also has taken the form of 
increasing the radius of curvature, so that the running 
of express-trains at a speed of 60 miles per hour will be 
facilitated. This is one of the comparatively rare cases 
where an increase in the radius of curvature justifies a 
considerable expenditure. 

Another illustration of the use of sharp curvature by a 
line of heavy traffic is given by the case of the B. & 0. R.R. 
in its line at Harper's Ferry. For many years the traffic 
of this road passed over two curves, one with a radius of 
300 feet (19° 10') and then over a 400-foot curve (14° 22'). 
During recent years this sharp curvature has been materi- 
ally reduced by means of some very expensive tunneling, 
•but the fact that the engineers of this line very wisely con- 
cluded to run the traffic of a great trunk line over such 
sharp curves shows how foolish it is for an engineer to 
sacrifice money or sacrifice gradients in order to reduce 
the rate of curvature on a road which at its best will be 
a line of very small traffic. Many locating engineers have 
started out to locate a line with instructions that their 
maximum rate of curvature must not exceed 6°. Pos- 
sibly it would be better to say that no limitation should 
be imposed. It is far better to operate a road on a 10° 
or 15° curve in some one place, provided that the cost of 
avoiding such a curve will be very large. This is especially 
true for the light-trafific roads, which constitute such a 
large proportion of our mileage, and which will probably 
constitute the great bulk of the roads yet to be constructed. 
Of course such belittling of the effects of curvature may 
be, and sometimes is, carried to an extreme and cause an 
engineer to fail to give to curvature its due consideration. 
Degrees of central angle should always be reduced by all 
the ingenuity of the engineer, and should only be limited 
by the general relation between the financial and topo- 
graphical conditions of the problem. Easy curvature is 



CURVATURE. 275 

in general better than sharp curvature and should be 
adopted when it may be done at a small financial sacrifice, 
especially since it reduces the length of the line. Never- 
theless the engineer should not give undue prominence to 
curvature in comparison with the other features of aline- 
ment, which are really of far greater importance. He 
should remember that so far as the cost of track-work is 
concerned, there is little if any saving in this respect, and 
that the extra cost of operating trains on curves is very 
nearly independent of the radius of curvature. Of course 
the trains cannot be operated at high speed on sharp 
curves, but if the road is a minor road such a condition 
will have almost no effect on the operation of trains. 
Above all, the engineer should not waste the capital of 
the road (which is usually limited) in an effort to avoid 
curvature, when any spare funds may more profitably 
be expended in making reductions of grade which will be 
of vastly greater financial value. 



CHAPTER XIV. 

MINOR GRADES. 

182. Two distinct effects of grade. — The effects of 
grade on train expenses are of two distinct kinds. One 
possible effect is very costly and should be limited even at 
considerable expenditure. The other is of comparatively 
little importance, its cost being slight. As long as the 
length of a train is not limited by the power of the engine, 
the occurrence of a grade on a road merely means that 
the engine is required to develop so many foot-pounds of 
work in raising the train so many feet of vertical height. 
For example, if a train weighing 600 tons (1,200,000 
pounds) climbs a hill 50 feet in height, the engine per- 
forms, in addition to the work due to mere tractive resist- 
ance and curvature, the extra work of creating 60,000,000 
foot-pounds of potential energy. If this height is sur- 
mounted in two miles of horizontal distance (grade of 25 
feet per mile) and in six minutes of actual time (20 miles 
per hour), the extra work accomplished by the engine is 
done at the rate of 10,000,000 foot-pounds per minute, 
which is about 303 horse-power. But the disadvantages 
of such a rise are always largely compensated. Except for 
the fact that one terminus of a road may be higher than 
the other, every up grade is followed more or less directly 
by a down grade, which is operated partly by the potential 
energy acquired during the previous climb. But when we 
consider the trains running in both directions, even the 

276 



MINOR GRADES. 277 

difference of elevation of the termini is largely neutralized. 
If we could eliminate altogether the waste of energy in 
the use of brakes, where brakes are used to control the 
train on grades, we would then find that the net effect of 
minor grades on either operation in both directions would 
be zero. Whatever was lost on any up grade would be 
regained on the succeeding down grade or on the retm-n 
trip. On the very lowest grades, the limits of which are 
defined later, we may consider this to be Hterally true, 
viz., that nothing is lost by their presence. It is unneces- 
sary to use brakes on these grades, except for such use as 
would be made if the line were level. Whatever energy is 
temporarily lost in climbing any grade is either imme- 
diately regained on a subsequent down grade or is regained 
on the return trip. 

The other effect of grade is that it may so limit the 
length of trains that more trains will be required to handle 
a given traffic. The receipts from traffic are a perfectly 
definite sum which is independent of the number of trains. 
The cost of handling the traffic will be nearly propor- 
tional to the number of trains. Anticipating a more com- 
plete discussion, it may be said, as an example, that in- 
creasing the ruling grade from 1.20% (63.36 feet per mile) 
to 1.55% (81.84 feet per mile — an increase of about 18.5 
feet per mile) will be sufficient to increase the required 
number of trains for a given gross traffic about 25%, 
i.e., five trains will be required to handle the traffic w^hich 
four trains would have handled before at a cost slightly 
more than four-fifths as much. Since the gross receipts 
remain the same and the operating expenses have been 
increased nearly 20%, the effect on dividends is readily 
imagined. On the other hand, a reduction of the grade, 
which will enable four trains to handle an amount of 
traffic w^hich have required five trains on the heavier 
grade, will have a corresponding influence in decreasing 



278 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

the operating expenses and will justify a large expenditure 
to accomplish this result. 

183. Basis of the cost of minor grades. — The basis of 
the computation of this least objectionable form of grade 
is as follows: The resistance to the movement of a train 
on a straight level track is variable, depending on the 
velocity, the number and character of the cars, and on 
the character of the road-bed and track. No one figure 
that can be stated may be considered accurate for all 
cases, but for average conditions and for average velocities 
we may consider that the round number of 10 pounds per 
ton is a reasonable figure. This value agrees fairly well 
with the results of some dynamometer tests made by 
Mr. P. H. Dudley, using a passenger-train of 313 tons 
running at about 50 miles per hour. It also agrees with 
Searles's formula (based on experiments) for the resist- 
ance of a freight-train with 40 cars running 25 miles per 
hour. Using the very approximate resistance formula 
published by the ^^Engineering News,'' which makes the 

resistance in pounds per ton equal to (2+^j, in which 

V is the velocity in miles per hour, this value would be 
true for a train moving at a speed of 32 miles per hour. 
A comparison of the three cases mentioned above shows 
at once the wide variations in the values given by different 
formulae. Therefore this value of 10 pounds per ton may 
be considered to be as nearly correct for an average value 
as any other one value that can be chosen. Ten pounds 
per ton is the grade resistance of a 0.5% grade, or a grade 
of 26.4 feet per mile. On this basis a 0.5% grade will 
just double the tractive resistalice on a straight level 
track. We may compute, as in the previous chapter, the 
cost of doubling the tractive resistance for one mile, but, 
since the extra resistance is due to lifting the train through 
26.4 feet of elevation, we may divide the extra cost of a 



MINOR GRADES. 279 

mile of 0.5% grade by 23.4 and we will have the cost of 
one foot of difference of elevation. If the rate of grade is 
not so great that it has an effect in limiting the length of 
trains, we may then say that the cost of this one foot of 
difference of elevation is independent of the rate of grade. 
On account of the compensating character of the effect of 
grade in the operation of trains down the grade or in the 
operation of a train down the other side of an elevation 
which has just been climbed, we must consider the total 
effect of one foot of rise and fall. Although we may say 
in a general way that the cost of one foot of rise and fall 
is independent of the rate of grade, it is true, as will be 
seen, that the cost of a foot of rise and fall of a very light 
grade is very much less than the cost of a foot of a much 
heavier grade. 

184. Meaning of " rise and fall." — In the simplest case 
a rise and fall of so many feet means a rise from the start- 
ing-point to a summit and a return to the same level, as 
is shown in Fig. 34. For instance, in Fig. 34 (a) is indi- 
cated a rise and fall of BD above the level AC, but (6) 
and (c) may be considered just as much cases of rise and 
fall. In (c) the line AB is actually an up grade, and yet 
we may consider it as a virtual drop. If a freight- train is 
moving up the grade in (6) and the engine is doing, the 
work which will carry it steadily up the grade ADC, it 
encounters additional resistance on the extra grade AB, 
and must either work much harder or it will continue to 
lose velocity. If it has sufficient momentum to carry it 
over the point B it will then continue on the grade BC, 
which, although an up grade, is so much less than the 
grade DC that the engine will do more work than is re- 
quired on such a grade and hence will gain velocity. This 
is essentially the same case as though a train were moving 
uniformly along the level (case a) and encountered the 
hump ABC. The case is essentially the same in (c). 



280 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

Although AB is actually an up grade, it is so much less 
than the grade ADC that if a train were running up that 
grade with the engine doing an amount of work which 
would carry it uniformly up the grade ADC, the resist- 
ance on the lesser grade AB will be so much less that the 
train will actually gain velocity and acquire a momentum 
which will enable it to climb the still steeper grade BC, 
so that by the time it reaches C it will have practically 
the same velocity which it had at A. We are therefore 





Fig. 34.— Types of "rise and fall". 

justified in considering that whether the train passes over 
a hump which is superimposed on an otherwise uniform 
grade, whether level or not, or goes through a sag which 
occurs in what would otherwise be a uniform grade, we 
may consider that in all cases the train is encountering 
what we denominate as ''rise and fall." When the line 
runs through a stretch of several miles with very light 
grades, all of which are well within the ruling grade, there 
is in general no possibility of doing anything which will 



MINOR GRADES- 281 

favorably affect the grade. Practically all that we can 
do is to remove what is virtually a hump or a sag in what 
is otherwise a nearly uniform grade or level. 

185. Classification of minor grades. — The additional 
cost of one foot of rise and fall is not altogether indepen- 
dent of the rate of grade. We can, however, divide grades 
into three groups, within which we may say that the cost 
of a foot of rise and fall is practically uniform. In the 
first class are grades which may be operated without 
changing the work of the engine, and which have practically 
no other effect than a harmless fluctuation of the velocity, 
but a grade which belongs to this class, when considering 
a fast passenger-train, will belong to another class when 
considering a slow and heavy freight-train, and, since it is 
the slow and heavy freight-trains which must be chiefly 
considered, a grade will usually be classified with respect 
to them. The limit of class A therefore depends on the 
maximum allowable speed, and also depends on the length 
of the grade and the depth of the sag. If it is permissible 
to operate all trains through the sag without making any 
change in the handling of the engine, without changing 
the throttle-valve or the position of the links, and espe- 
cially without the use of brakes, then the effect of the sag 
on the operation of trains is possibly zero, and the sag or 
hump has no financial importance. The above conditions 
assume that the engine is working uniformly throughout, 
that all potential energy which is lost on the steeper grade 
is regained on the lighter grade. In the case of a sag the 
change in potential energy merely comes in reversed order. 
If train resistance and tractive effort were actually inde- 
pendent of velocity, the assumption that class A has no 
influence on train expenses would be almost theoretically 
precise. The operation of momentum grades has been 
considered in Chapter XI. In classifying a sag or a hump 
we must therefore consider whether trains which run over 



282 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

or through it may be operated without changing any 
operating conditions. We will very often discover that 
passenger-trains may be so operated, while freight-trains 
will need to be handled differently. Therefore such a hump 
or sag will be classified as belonging to class A for pas- 
senger-trains, and to class B or possibly class C for freight- 
trains. 

The next classification (B) applies to grades on which 
a change of operating conditions becomes necessary. On 
the dow^n grade it becomes necessary to partially, if not 
entirely, close the throttle, in order that the velocity shall 
not become too great. On the other hand, the up grade 
•is so steep that the engine must work considerably harder, 
consume more coal, and perhaps operate with a longer 
cut-off and therefore less economy than is possible on the 
lighter grades. As long as brakes are not used there is 
no actual loss of energy, except that steam v/ill probably 
be wasted by being blown through the safety-valve while 
the train is running down the grade with the throttle 
closed. The chief disadvantage is due to the uneconomical 
working of the train on the heavier up grade. On the 
down grade the losses in fuel consumption, due to radia- 
tion, etc., will become a much larger percentage than 
usual of the useful work actually obtained from the engine. 

The third class (C) includes humps which are so high 
and sags which are so deep that brakes must be applied 
on the down grade in order to prevent excessive velocity. 
The loss by the application of brakes is very heavy. The 
brakes require power for their application which is a con- 
siderable tax on the locomotive. The use of brakes cauess 
wear of the brake-shoes and of the wheel-tires, which 
hastens the deterioration of the rolling-stock. Their use 
destroys the kinetic or potential energy which had pre- 
viously been created, wiiile the tax on the locomotive on 
the corresponding ascending grade is very great. 



MINOR GRADES. 283 

It may be seen that the classification of these humps 
and sags is more a matter of the total height of the hump 
or the depth of the sag rather than the rate of grade. 
The sag or hump which has a comparatively steep grade 
on both sides may be almost harmless if the grades are 
short, or (which amounts to the same thing) if the height 
or depth is small. On the other hand, a comparatively 
light grade may become of importance because it is so 
deep. It is not usual, however, that a sag or hump could 
be classified in class C if the grade is very light, since it 
requires a considerable grade to cause a train to attain a 
dangerous velocity when the steam is turned off. Exces- 
sively long sags or humps are practically outside of the 
line of problems which may thus be considered. 

i86. Effect on operating expenses.^As in the previous 
chapter we may at once throw out a large proportion of 
the items of expense of an average train-mile. In ^'main- 
tenance of way and structures " Items 4 to 10 are evi- 
dently unaffected. The other items will be variously 
affected according to the classification of grades. 

187. Item I. Repairs of roadway. — It is very plain 
that a large proportion of the subitems are absolutely 
unaffected by minor grades. In fact it is a little difficult 
to ascribe any definite increase to any subitem. Rail 
wear is somewhat increased and this will have some effect 
in increasing the track-work. Wellington allows 5% in- 
crease as a liberal estimate for class C, and makes no 
allowance for classes A and B. 

188. Item 2. Renewals of rails. — Observations of rail 
wear on heavy grades show that the wear is much greater 
than on level tangents. The heavy grades of a mountain 
division of a road are usually operated w^ith shorter trains 
or with the help of pusher-engines, and in such cases the 
proportion of engine tonnage to the total is much greater 
than on minor grades, and, since the engine has much 



284 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

greater effect on rail wear than an equal total tonnage of 
cars, partly on account of the use of sancl and excess of 
engine tonnage, the grade will have a marked effect on 
rail wear. But such circumstances apply to ruling grades 
and very little, if at all, to minor grades. The use of sand 
on up grades and the possible skidding of wheels on down 
grades will wear the rails considerably. Even the slipping 
of the drivers, although sand is not used, will wear the 
rails. Wellington allows 10% increase for class C and 
5% for class B. 

189. Item 3. Renewals of ties. — The extra wear of 
ties on grades is considered by Wellington as being some- 
what compensated by the improved drainage of the road- 
bed which is found on a track which is not quite level, 
the better drainage tending to increase the life of the ties. 
On this account Wellington made an allowance of 5% 
increase for class C and no increase for the other classes. 

190. Maintenance of equipment. — It is evident that 
none of these items will be affected except Items 12 to 15, 
^' the repairs and renewals of engines and cars." The chief 
effect on these items will evidently be the repairs and 
renewals of wheels and brake-shoes. The draw-bars are 
also apt to suffer somewhat, on account of the increased 
work which they are required to do. It would appear 
that the extra stress on the locomotive mechanism will 
have some effect on locomotive repairs, and the expense 
of boiler repairs may be increased on account of the greater 
range of the demands on it. It would seem as if such 
effects would be quite large, but if the records of engine 
and car repairs on mountain divisions and on compara- 
tively level divisions of the same road are examined and 
compared, there appears to be no such difference as might 
be expected. Considering the very small proportion of 
locomotive and car repairs which are affected at all by 
such circumstances, and also the very small percentage 



MINOR GRADES. 285 

of these subitems which can be said to be affected by 
these two classes of minor grades, Welhngton allows only 
an increase of 4% on each of these four items for class C 
and 1% for class B. 

191. Conducting transportation. — It is apparent that 
the only items in conducting transportation which will be 
affected will be the four items of engine-supplies (22 to 
25). As in Chapter XIII, since we are considering that 
the resistance is doubled, we will assume that there is an 
increase of 44% as the cost of the extra fuel used in climb- 
ing 26.4 feet, but the total cost of both rise and fall is to 
be considered. In class B, although steam is shut off, 
fuel will be wasted by mere radiation. On this account 
we will add 5%. For class C we must allow in addition 
the energy spent in applying the brakes, which we may 
assume as 5% more. Therefore we will allow 49% for 
class B and 54% for class C. The other small items of 
supplies, 23, 24, and 25, will be estimated similarly. The 
items of general expense are evidently unaffected. 

192. Estimate of cost of one foot of change of elevation. 
— Collecting the above estimates we have Table XXVI, 
showing that the percentage of increase for operating 
grades of classes S or C will be 5.89%, and 7.70%o 
respectively of the average cost of a train-mile. On the 
basis of an average cost of $1.30 per train-mile, the addi- 
tional cost for the 26.4 feet of rise and fall m one mile 
would be 7.66 c. and 10.01 c, or 0.29 c. and 0.38 c. per 
foot for the two classes respectively. For each train per 
day each way per year the value per foot of difference of 
elevation is 

For class B: 2 X365x $0.0029 = 12.12. 
'' '' C: 2X365X$0.0038 = $2.77. 

In assuming the number of trains running over a given 
grade the character of the trains must be carefully con- 



286 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

sidered, since it will quite frequently happen that a hump 
or sag must be classified as belonging to class (7, so far as 
heavy freight-trains are concerned, but may be classified 
as B or perhaps even A, the harmless class, for passenger- 
trains. The above values should likewise be modified 
when the trains are run only 313 days per year instead of 
365. 



Table XXVI.- 



-Effect on Operating Expenses of 26.4 Feet of 
Rise and Fall. 





Item (abbreviated). 


Normal 
average. 


Class B. 


Class C. 


No. 




u 

1^ 






1 


Roadway 


10.767 
1.422 
2.948 
5.897 



5 






.071 






5 

10 

5 




.538 


2 


Rails 


.142 


3 


Ties 


.147 


4-10 


Bridges, buildings, etc 

Maintenance of way. 







21.034 




.071 




.827 








11 


Superintendence 


.617 
6.538 
2.174 
7.160 

.198 
1.337 




1 
1 
1 
1 




.065 
.022 
.072 
.002 






4 
4 
4 
4 






12 
13 
14 


Repairs, locomotives 

Repairs, passenger-cars 

Repairs, freight-cars. . 


.261 

.087 
.286 


15 


' ' work-cars. . 


.008 


16-19 


Miscellaneous 







Maintenance of equipment. . . 






18.024 




.161 




.642 


20 


Superintendence 


1.757 
9.607 

10.316 
1.226 

33.730 






49 

49 








5.055 

.601 








54 

54 







21 


Enginemen 





22 


Fuel 


5.571 


23-25 


Water, oil, etc 


.662 


26-46 


Train-service, etc 







Conducting transportation. . .. 






56.636 




5.656 




6.233 


47-53 


General expenses 


4.306 


















100.000 


... 


5.88F 




7.702 



193. Numerical illustration. — Assume that the grade 
of a raihoad in crossing a river valley includes a sag 5000 



MINOR GRADES. 287 

feet long and with a depth in the center of 40 feet. Assume 
that freight-trains would ordinarily approach this sag at 
a velocity of 20 miles per hour. The velocity head at 20 
miles per hour, as found in Table XX, is 14.05 feet. Add- 
ing the depth of the sag, 40 feet, we would have the velocity 
head at the bottom of the sag, 54.05 feet, which corre- 
sponds to a velocity of over 39 miles per hour. The exten- 
sive adoption of automatic couplers and train-brakes have 
permitted the use of much higher freight-train speeds than 
were permissible some years ago. Even though it might 
be considered safe to run the train through the sag at a 
speed of nearly 40 miles per hour, it is unquestionable 
that a freight-engine could not develop steam fast enough 
to exert a constant draw-bar pull up to a speed of 39 miles 
per hour. There would therefore be a very considerable 
loss from the theoretical operation of such a sag as de- 
scribed above, and we must consider that the sag will not 
belong to class (A), at least for freight-trains. If a pas- 
senger-train approached this sag at a velocity of 30 miles 
per hour, the velocity head then being 31.60 feet, its 
velocity head at the bottom of the sag would be 71.60, 
which would correspond to a velocity of over 45 miles per 
hour. If the passenger-engine were so lightly loaded that 
its draw-bar pull at the top of the sag was quite small, 
and its boiler capacity was so large that it could develop 
this light draw-bar pull even at a speed of 45 miles per 
hour, then for such trains we could consider the sag as 
belonging to class {A), the harmless class. Assume that 
after an analysis of the character of the trains using the 
sag, we find there are six trains per day each way in the 
operation of which the sag should be classed as class (C), 
and eight other trains per day each way for which it should 
be classed as class (5). It should be noted that it is not 
essential to fill up the sag altogether and make it level. 
If we fill up only the lower 20 feet, which will not ordinarily 



288 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

cost more than one-fourth to one-third as much as filUng 
up the upper 20 feet, the sag would probably become 
harmless for all classes of trains. We will therefore com- 
pute the value of reducing the depth of the sag 20 feet. 
We will have the added cost of operating this 20 feet as 
follows : 

Eight trains, class (B): 8 X 20 X $2.12 = $339.20 
Six " " (C): 6 X 20 X $2.77 = $332.40 



Total annual saving. . . . .• $671.60 

Capitalizing this at 5%, we have $13,432 as the justifiable 
expenditure to fill up the lower 20 feet of this sag. Of 
course the amount of earthwork required to make this 
fill can be readily computed. In the case of a new road 
we would have merely this additional cost to the original 
plan of construction. If such a plan is considered with 
the intention of improving an old line, the cost of raising 
the track, and all the added expense involved in maintain- 
ing the track so that traffic may continue to run over it, 
will have to be added as part of the cost of improvement. 
The cost of such an improvement is a comparatively 
simple matter to determine. The above demonstration, 
even though it is based on data which is approximate, is 
at least a measure of the value of the improvement, which 
is far better than having no measure at all. In applying 
the method outlined above to any particular case, the 
problem must be studied from the beginning with refer- 
ence to all the available figures of cost as applied to the 
given road. The figures given above for the value of one 
foot of rise and fall of either class should not be used in 
general for all cases, and in fact should never be used ex- 
cept as an approximate method for computing the value of 
a change in the proposed location of a new road where there 
is no data on which to base more accurate calculations. 



CHAPTER XV. 

RULING GRADES. 

194. Definition. — Ruling grades are those which Hmit 
the weight or length of a train of cars which may be hauled 
by one engine. They are frequently, although not neces- 
sarily, the steepest grades on the road. It is sometimes 
possible by a mere change in the method of operating the 
trains to very greatly reduce what must technically be 
considered the ruling grade of the road. When one or two 
grades on the road are considerably higher than all other 
grades, it is possible to use assistant engines on those 
grades, and thereby very greatly increase the weight or 
number of cars in a through-train load over the entire 
line. The weight of train will then be limited by the next 
lower grade, which may be a grade which offers but little 
more than one-half the total resistance of the grade which 
is operated by pusher-engines. This enables the train-load 
to be practically doubled. Such grades, which are called 
pusher grades, will be considered in a succeeding chapter. 

When a grade is very short and it is never necessary to 
stop a train while on the grade, it is frequently possible to 
load up an engine with a far greater number of cars than 
could be run up an indefinite grade of that length. This has 
already been discussed in the chapter on Momentum 
Grades. These are the most common exceptions to the 
general statement that the ruling grade is usually the 
maximum grade of the road. 



290 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

The selection of the general route of the road usually 
determines more or less definitely the ruling grade of the 
road, except as that may be modified by ^'development." 
The rate of ruling grade should bear some relation to the 
general character of the road which is to be built. A 
second-class or third-class road, which at its best will 
never be anything more than a branch fine, is not justified 
in spending much money to reduce a ruling grade. On 
the other hand, a great trunk line is thoroughly justified 
in spending enormous sums in the construction of tunnels, 
deep cuts, high embankments or viaducts, in order to 
reduce the rate of the ruling grade. In this chapter we 
will endeavor to determine the financial relation between 
the lowest permissible grade and the money which may 
profitably be spent to secure it. 

195. Choice of ruling grade. — A little consideration re- 
garding the practical operation of trains will show that it 
is impracticable for an engine to drop off or pick up cars 
in accordance with the grades which may be encountered 
along the line. The nearest approach to this is to divide 
a long road into divisions. At the termini of each division 
are located freight-yards at which the cars are assorted, 
and, if necessary, the train-load is increased or diminished, 
according to the capacity of the engines which are to haul 
the trains over the succeeding division. The locating 
engineer cannot determine the proper rate of ruling grade 
for a line until after the belt of country through which the 
road is to pass has been thoroughly surveyed, and he can 
study the project as a whole. There are usually a dozen or 
more points within a distance of 100 miles through which 
a railroad is almost compelled to pass, and which must be 
considered as governing points, unless there is very urgent 
reason why the road should not go through them. The 
selection of the rate of grade then becomes a problem of 
determining the best route between each pair of consecu- 



RULING GRADES. 291 

tive governing points. If the natural grade between two 
consecutive points is very high, and much higher than the 
grades between other consecutive ruling points, it may be 
advisable to immediately decide to operate the especially 
steep grade wath pusher-engines, and thereby make it 
possible to use a much lower rate for the ruling grade. 
The endeavor should be made to cut down all grades 
which would naturally be somewhat higher than the other 
grades until a considerable number of grades have been 
determined, all of which are approximately equal and 
which cannot be materially reduced without a large 
expenditure. On the one hand, it will not pay to spend 
any amount of money to reduce a grade below this maxi- 
mum which has been selected, although, on the other hand, 
it will pay to spend considerable to cut down the rate of 
grade on one or two grades which are higher than the gen- 
eral maximum. In this way may be determined, after 
considerable study, some Hmit of grade which can be used 
at all points without an extravagant expenditure of money, 
and yet which could not be reduced, on account of the 
large number and length of the grades which would be 
involved, without an extravagant expenditure of money. 
The engineer is frequently confronted with a definite prob- 
lem substantially as follows: The rate of ruHng grade at 
one or two places on the line is naturally at some definite 
figure, say, 1 .4% . By spending an easily computable sum of 
money the line may be modified so that the ruling grade is 
reduced to perhaps 1 .0% . The engineer must then consider 
the traffic to be run over the road, and must compute the 
effect on the operating expenses of reducing the rate of grade. 
If the annual saving in operating expenses,when capitalized 
materially exceeds the cost of obtaining the lower grades, 
it will probably be justifiable to construct them. 

196. Maximum train -load on any grade. — The tractive 
power of a locomotive, and especially the reduction of t-he 



292 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

effective tractive power with increase in velocity, has 
already been discussed in previous chapters. It is ex- 
pected that on ruling grades a train runs slowly if necessary. 
Fortunately the tractive power of a locomotive is greatest 
when the speed is slow, and when very nearly the full 
theoretical adhesion of the drivers to the rails can be 
counted on. In Table XXVII are given the tractive 
powers of locomotives of a wide range of types and weights 
and with various ratios of adhesion. Almost any loco- 

Table XXVII. — Tractive Power of Various Types of Standard- 
gauge Locomotives at Various Rates cf Adhesion. 



Type of Locomotive. 



Atlantic, 4-4-2 

Atlantic, 4-4-2, four-cyl- 
inder compound 

Pacific, 4-6-2 

Pacific, 4-6-2 

Ten- wheel, 4-6-0 

Prairie, 2-6-2 

Consolidation, 2-8-0. . . 
Consolidation, 2-8-0. . . 
Mikado, 2-8-2 



Total weight 

of engine and 

tender. 



Lbs. 



340,000 

368,800 
343,600 
403,780 
321,000 
366,500 
214,000 
366,700 
405,500 



Tons. 



170.0 

184.4 
171.8 
201.9 
160.5 
183.2 
107.0 
183.3 
202.7 



Weight 

of 
engine 
only. 



199,400 

206,000 
218,000 
226,700 
201,000 
212,500 
120,000 
221,500 
259,000 



Weight 
on the 
drivers. 



105,540 

115,000 
142,000 
151,900 
154,000 
154,000 
106,000 
197,500 
196,000 



Tractive power when 
ratio of adhesion is 



1/4 



26,385 

28,750 
35,500 
37,975 
38,500 
38,500 
26,500 
49,375 
49,000 



9/40 



23,740 

25,875 
31,950 
34,180 
34,650 
34,650 
23,850 
44,440 
44,100 



1/5 



21,100 

23,000 
28,400 
30,380 
30,800 
30,800 
21,200 
39,500 
39,200 



motive will be sufficiently similar to one of these given in 
this table, so that the tractive force here given may be 
used for calculations, at least approximately. In Table 
XXVIII is shown the total train resistance in pounds per 
ton for various grades and for various values of track 
resistance. By a combination of these two tables the net 
train-load on any grade under given conditions may be 
quickly determined. For example, a consolidation engine, 
weighing 214,000 pounds and having 106,000 on the 
drivers, will have a tractive power of 23,500 pounds when 
the effective adhesion is J. When it is moving slowly up 
a 1.2% grade the grade resistance is 24 pounds per ton, 
and if the tractive resistance on a level is 6 pounds per 



RULING GRADES. 293 

ton the total train resistance per ton will be 30 pounds. 
Dividing 23,500 by 30, we have 883 pounds as the gross 
train-load. Subtracting 107 tons, the weight of the engine 
and tender in working order, we will have 776 tons as the 
net load. A much better way of considering this will be 
on the basis of rating tons, as already explained in Chapter 
XI, but, whatever the method adopted. Tables XXVII and 
XXVIII are accurate as long as the velocity is so slow 
that the boiler capacity is not overtaxed, and as long as 
the proper ratio of adhesion and the actual tractive resist- 
ance on a level are chosen for use in the tables. 

197. Proportion of traffic affected by the ruling grade. 
— Very many hght-traffic roads are not fortunate enough 
to have a traffic which is materially affected by the rate of 
ruling grade. Passenger- trains are very seldom affected, 
unless the volume of traffic is so great that the number of 
cars attached to one engine approaches the limit which 
one engine is able to haul. The comparatively high speed 
usually demanded of passenger-trains means that the 
locomotive must have high steaming power to haul even 
light loads. Such hght loads do not require very great 
tractive force, and therefore the tax on the adhesion of 
the drivers is correspondingly small. When a passenger- 
train reaches an unusually heavy grade, the effect of the 
grade is usually confined to reducing the speed of the 
train. On any road but a trunk line such a slight reduc- 
tion of speed has almost no financial value. We may 
therefore make the general statement that for all light- 
traffic roads the passenger-trains need not be considered 
as being affected by the rate of ruling grade. Local 
freight- trains may sometimes be considered in the same 
way. It frequently happens that the local freight is sent 
out over the line with a far less number of cars than could 
be hauled by one engine, and therefore the ruling grades 
cannot be considered as affecting these trains. Whatever 



294 THE ECONOMICS OF RAILROAD CONSTRUCTION. 



Table XXVI II. — Total Train Resist.^ce per Ton (of 2000 
Pounds) on Various Grades. 



When tractive resist- | 




When tractive resist- 


Grade. 


ance on a 


level in 


Grade. 


ance on a level in 




pounds per ton is 1 




pounds per ton is 


Rate 


Feet 




! 








Rate 


Feet 












per 


per 


6 


7 


8 


9 


10 


per 


per 


6 


7 


8 


9 


10 


cent. 


mile. 












cent. 


mile. 








4C 




0.00 


0.00 


6 


7 


8 


9 


10 


2.00 


105.60 


46 


47 


48 


50 


.05 


2.64 


/ 


8 


9 


10 


11 


.05 


108.24 


47 


48 


49 


5C 


51 


.10 


5.28 


8 


9 


10 


11 


12 


.10 


110.88 


48 


49 


50 


51 


52 


.15 


7.92 


9 


10 


11 


12 


13 


.15 


113.52 


49 


50 


51 


52 


53 


.20 


10.56 


10 


11 


12 


13 


14 


.20 


116.16 


50 


51 


52 


5?. 


54 


025 


13.20 


11 


12 


13 


14 


15 


2.25 


118.80 


51 

52 


52 
53 


53 
54 


54 
55 


55 


.30 


15.84 


12 


13 


14 


15 


16 


.30 


121.44 


56 


.35 


18.48 


13 


14 


15 


16 


17 


.35 


124.08 


53 


54 


55 


56 


57 


.40 


21.12 


14 


15 


16 


17 


18 


.40 


126.72 


54 


55 


56 


57 


58 


.45 


23.76 


15 


16 


17 


18 


19 


.45 


129.36 


55 


56 


57 


58 


59 


0.50 


26.40 


16 


17 


18 


19 


20 


2.50 


132.00 


56 


57 


58 


5c 


60 


.55 


29.04 


17 


18 


19 


20 


21 


.55 


134.64 


57 


58 


59 


60 


61 


.60 


31.68 


18 


19 


20 


21 


22 


.60 


137.28 


58 


59 


60 


61 


62 


.65 


34.32 


19 


20 


21 


22 


23 


.65 


139.92 


59 


60 


61 


62 


63 


.70 


36.96 


20 


21 


22 


23 


24 


.70 


142.56 


60 


61 


62 


63 


64 


0.75 


39.60 


21 


22 


23 


24 


25 


2.75 


145.20 


61 


62 


63 


64 


65 


.80 


42.24 


22 


23 


24 


25 


26 


.80 


147.84 


62 


63 


64 


65 


66 


.85 


44.88 


23 


24 


25 


26 


27 


.85 


150.48 


63 


64 


65 


66 


67 


.90 


47.52 


24 


25 


26 


27 


28 


.90 


153.12 


64 


65 


66 


67 


68 


0.95 


50.16 


25 


26 


27 


28 


29 


.95 


155.76 


65 


66 


67 


68 


69 


1.00 


52.80 


26 


27 

28 


28 
29 


29 
30 


30 
31 


3.00 


158.40 


66 


67 


68 


69 


70 


.05 


55.44 


27 


.05 


161.04 


67 


68 


69 


70 


71 


.10 


58.08 


28 


29 


30 


31 


32 


.10 


163.68 


68 


69 


70 


71 


72 


.15 


60.72 


29 


30 


31 


32 


33 


.15 


166.32 


69 


70 


71 


72 


73 


.20 


63.36 


30 


31 


32 


33 


34 


.20 


168.96 


70 


71 


72 


73 


74 


1.25 


66.00 


31 


32 


33 


34 


35 


3.25 


171.60 


71 


72 


73 


74 


75 


.30 


68.64 


32 


33 


34 


35 


36 


.30 


174.24 


72 


73 


74 


75 


76 


.35 


71.28 


33 


34 


35 


36 


37 


.35 


176.88 


73 


74 


75 


76 


77 


.40 


73.92 


34 


35 


36 


37 


38 


.40 


179.52 


74 


75 


76 


77 


78 


.45 


76.56 


35 


36 


37 


38 


39 


.45 


182.16 


75 


76 


77 


78 


79 


1.50 


79.20 


36 
37 


37 

38 


38 
39 


39 
40 


40 
41 


3.50 


184.80 


76 


77 


78 


79 

89 


80 


.55 


81.84 


4.00 


211.20 


86 


87 


88 


90 


.60 


84.48 


38 


39 


40 


41 


42 


4.50 


237.60 


96 


97 


98 


99 


100 


.65 


87.12 


39 


40 


41 


42 


43 


5.00 


264.00 


106 


107 


108 


109 


110 


.70 


89.76 


40 


41 


42 


43 


44 


5.50 1290.40 


116 


117 


118 


119 


120 


1.75 


92.40 


41 


42 
43 


43 
44 


44 
45 


45 
46 


6.00 


316.80 


126 


127 


128 


129 


130 


.80 


95.04 


42 


6.50 


343.20 


136 


137 


138 


139 


140 


.85 


97.68 


43 


44 


45 


46 


47 


7.00 1.369.60 


146 


147 


148 


149 


150 


.90 


100.32 


44 


45 


46 


47 


48 


8.00 


422.40 


166 


167 


168 


169 


170 


1.95 


102.96 


45 


46 


47 


48 


49 


9.00 


475.20 


186 


187 


188 


189 
209 


190 


2.00 


105.60 


46 


47 


48 


49 


50 


10.00 !528.00 


12061207 


208 


l210 



RULING GRADES. 295 

business is done by the road in handling bulky freight, 
such as coal, ore, or timber, is usually handled in train- 
loads which are made as heavy as the power of the engine 
on the grades of the road will permit. All such trains are 
directly affected by the rate of ruUng grade. Therefore, 
in counting the number of trains which are affected by the 
ruling grade, we must usually count all coal-, lumber-, and 
ore-trains, and all through freight-trains which are run 
from one terminus of the division to another, as well as 
passenger-trains, if any, which are actually limited in 
length or weight by the grade. 

198. Financial value of increasing the train-load. — 
The gross receipts obtained for transporting a given 
amount of freight is a definite sum which is independent 
of the number of train-loads required to handle it. On 
the other hand, the cost of a train-mile is nearly constant. 
If it were actually so, we could say at once that the cost 
of handling the traffic would be proportional to the number 
of trains, and that the saving of even one train-load, or 
of handling in four trains what would otherwise require 
five train-loads, would reduce the operating expenses pro- 
portionally. The problem is a very similar one to that 
already worked out in Chapter VII, but with a very 
important difference in some of the conditions. In both 
cases the object to be gained is the reduction in the number 
of trains to handle a given gross tonnage of freight traffic 
In the case worked out in Chapter VII, this is accom- 
plished by merely increasing the power of the locomotives, 
so that a given amount of traffic can be handled in three 
trains instead of four, or in six trains instead of seven, the 
grades of the road being the same in each case. By the 
method discussed in this chapter, the grade is so reduced 
that an engine of given type may haul a larger number of 
cars, and therefore a certain gross amount of freight ton- 
nage can be handled in three trains instead of four, or in 



296 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

six trains instead of seven, using engines of the same type 
and weight. In the first case, the power of the engine is 
increased; in the second case, the demand on its capacity- 
is reduced by a reduction in the grade. 

We will estimate as before the difference in the cost of 
operating, say, four light trains on heavy grades, or three 
heavier trains on the lighter grades. In either case the 
gross tonnage of cars, with their contents, is supposed to 
be the same. The difference consists in the cost of operat- 
ing the extra engine and also the extra cost for train 
service, etc., which is a function of the number of trains 
on the road rather than of their tonnage. For the same 
reasons as are given in detail in § 86, we will consider that 
the items in maintenance of way will be affected the same 
as is there computed, namely, 3.531%. 

199. Maintenance of equipment. — We will consider that 
Item 11 is unaffected. While there is some ground for 
considering that using four engines instead of three for a 
given gross tonnage of freight is actually somewhat of an 
advantage in some respects, since it reduces the work of 
the locomotive throughout the level sections of road, it is 
not safe to allow very much on this account. If, on 
account of the reduction in average draw-bar pull, the 
repairs of each of four locomotives were reduced 5% below 
the repairs of the three locomotives which could haul the 
same number of cars over lower ruling grades, then the 
repairs of the four locomotives would cost 4X95, or 380 
compared with 3X100, or 300 for the three locomotives. 
This would mean that the additional locomotive should be 
assigned an added expenditure of 80% of the average 
cost for one. If the saving by the reduction of grade was 
only half as much, or one train in eight, so that seven 
trains were required to do the work of eight on the steeper 
grade, then the saving per engine would be correspondingly 
less. If it were 2.5% instead of 5, we would have, for the 



RULING GRADES. 297 

cost of eight engines, 8 X 97.5, or 780 compared with 7X 100, 
or 700 for the seven engines. Again, we would have 80% 
as the additional net cost of the repairs on the additional 
engine. Of course the above estimates of 5% and 2.5%, 
as the saving on one engine, are merely guesswork, but 
the above demonstration shows that if the saving in 
repairs is proportional to the reduction in number of 
trains which is made possible by the reduction of grade, 
as is quite probable, then the cost of the repairs of the 
extra engine is the same, whether it is one engine out of 
four, or one engine out of eight, or one engine out of any 
other number. Therefore, although the estimate of 5% 
per engine as made above is a guess, it is probably near 
enough to the truth, so that there is comparatively little 
error in using the figure of 80% for the additional cost of 
repairs of the additional engine. 

The item of repairs of passenger-cars may or may not 
be affected, depending on whether the reduction of grade 
will actually affect the number of passenger-cars attached 
to a train. On trunk lines, when many of the most popular 
through express-trains must be operated in sections, 
because their length is actually limited by the rate of 
ruling grade, this item must be considered for its full 
value for as many trains as will be affected. But, on the 
large majority of the roads of the country, this item will 
be absolutely unaffected, and it will therefore be ignored 
in this calculation. Item 14, ^^ repairs and renewals of 
freight-cars, '^ will actually be reduced by the policy of 
reducing the number of cars hauled by one engine. Al- 
though the maximum draw-bar pull of the locomotive, and 
therefore its pull on the first car behind the engine, will 
be the same in either case, yet the average draw-bar pull 
for the lighter trains will be considerably less, and this 
will have its effect on the repairs of the draw-bar mechan- 
ism. A reduction in the weight of train will also have its 



298 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

effect on the cost of repairs, clue to concussion and many 
other similar causes. The amount of this redu^ion is a 
matter almost of guesswork, as was also the reduction in 
the cost of the repairs of locomotives. Wellington claims 
that the cost of the repairs of the freight-cars involved 
would equal 10%, and we will therefore take that figure 
as a negative addition to the cost of operating the extra 
train. The other items of maintenance and equipment 
are evidently unaffected. 

200. Conducting transportation. — Items 20, ^' cost of 
superintendence," will be practically unaffected. Item 
21, '' the wages of enginemen," will be given its full value. 
The additional cost for the fuel for the added engine may 
be computed somewhat on the same basis as the cost of 
engine repairs. The fuel used by four engines will average 
somewhat less than that used by three engines, since the 
four engines will do far less work on the level and on very 
light grades, while on the heavier grades the engines are 
working to the limit of their capacity in either case. The 
loss of heat, due to radiation and the other causes, which 
are independent of the direct work done by the engine in 
hauling, will be the same in either case. These causes 
have already been discussed in § 142. It is impossible to 
make any general calculations as to the relative consump- 
tion of fuel in the two cases, since so much depends on 
the proportion of track w^hich is level or which has a very 
light grade. If the four engines operating hghter trains 
each burn 5% less fuel than three engines operating 
heavier trains, we will find, by the same method as before, 
that the extra engine may be charged with 80% of the 
average fuel consumption of the other three engines. If, 
as before, we assume that this variation in fuel consump- 
tion is proportional to the variation in the number of 
trains required to handle a given traffic, then the extra 
engine would be responsible for 80% of the average fuel 



RULING GRADES. 299 

consumption, regardless of whether the number of trains 
saved was one in four or one in ten. Although it is true 
that the value 80% is a mere guess, that no general value 
is obtainable, and that the value for any particular and 
special case could only be computed with great diffi- 
culty, it is evident that the error is not very great, and we 
will therefore assume 80% as the fuel consumption assign- 
able to the extra engine. The consumption of other 
engine-supplies, water, oil, waste, etc., is not strictly pro- 
portional to the consumption of fuel, but we will assume 
it to be so in this case, and that 80% of Items 23-25 
are allowable for the extra engine. 

Items 26 to 32, which concern train-service, will be con- 
sidered as varying according to the number of train-miles, 
and we will therefore add 100% for all these items. The 
item of car-mileage is evidently unaffected. Items 33-37, 
which refer to damages, might be considered from one 
standpoint to be unaffected, while from other standpoints 
the effect might be considered as 100%. The risk of train 
operations varies very largely with the number of trains, 
and yet in some respects the danger is independent of 
whether there are 15 or 20 cars in a train. There will be 
little error in assigning 50% extra for this item. Items 
38 to 44 are evidently unaffected. Items 45 and 46 will 
be considered as affected 50%. The general expenses are 
evidently unaffected. Collecting these various items we 
have Table XXIX. To this we will add, as before com- 
puted, an average charge of 0.25 c. per mile as the mile- 
age charge for the capital cost of the extra engine. 

If we assume that the average cost of a train-mile is 
$1.30, then the operating value per mile of saving the 
use of the additional engine equals 51.757% of $1.30, or 
67.28 c. Adding 1.25 c. for the cost of the engine, we 
have 68.53 c, which we will call 69 c. 



300 THE ECONOMICS OF RAILROAD CONSTRUCTION. 



Table XXIX. — Additional Cost of Operating a Given Freight 
Tonnage with Four Engines on Heavy Ruling Grades in- 
stead OF WITH Three Engines on Lighter Grades. 



No. 


Item (abbreviated). 


Normal 
average, 
per cent 


Per cent 
affected. 


Cost per 
cent. 


1 


Roadway 


10.767 
1.422 
2.948 
2.461 
3.436 


12.5 

50 

50 






1.346 


2 


Rails 


.711 


3 


Ties 


1.474 


4 
5-10 


Bridges and culverts 

Buildings, etc 














Maintenance of way 


21.034 





3.531 








11 


Superintendence 


.617 
6.538 
2.174 
7.160 
1.535 




80 



-10 







12 

13 

14 

15-19 


Repairs of locomotives 

" " passenger-cars. . . . 

* ' " freight-cars 

Miscellaneous 


5.230 


-.716 











Maintenance of equipment. . . 


18.024 





4.514 


20 


Superintendence 


1.757 
9.607 
11.542 
23.149 
1.829 
2.288 
5.307 
1.157 




100 

80 

100 



50 



50 





21 


Enginemen. . . . 


9.607 


22-25 


Fuel, etc 


9.234 


26-32 


Train-service, etc 


23.149 


33 


Car-mileage 





34-37 


Damages, etc 


1.144 


38-44 


Miscellaneous 





45-46 


Stationery etc 


.578 










Conducting transportation. . .. 


56.636 




43.712 


47-53 


General expenses 


4.305 





0. 









100.000 



51.757 



201. Numerical illustration. — As a practical illustration 
of the above figures assume that the ruling grade on a 
given hne is 1.4% (73.72 feet per mile). Assume that only 
8 trains per day out of a total of 20 trains of all kinds 
are to be considered as affected by the rate of the ruling 
grade. Assume that it has been discovered that with the 
expenditure of $300,000 a change of alinement may be 
made which will reduce the ruling grade to 1%. Is such 
an expenditure justifiable under the circumstances? It 
has been shown in the chapter on Train Resistance that the 



RULING GRADES. 301 

actual tax on the locomotive depends quite largely on the 
ratio of live load to tare. Therefore the only comparison 
which can justifiably be made as the basis for planning 
construction is to assume the same conditions of loading 
for both cases. For this comparison we will assume the 
resistances taken from Mr. Dennis's paper, as already 
referred to in Chapter XI, §§ 128-133. The grade and 
tractive resistance for a rating ton on the 1.4% grade 
would be (28.0 + 2.6), or 30.6 pounds per ton. The tract- 
ive power, as given for Mr. Dennis's locomotive at the 
speed of 7 miles per hour, is 28,200 pounds. The gross 
rating tons which could be hauled at this speed therefore 
equals (28,200-^30.6), or 922 gross rating tons. The ratio 
of a tare ton to a rating ton on a 1.4% grade equals 121% 
(see § 129). The actual weight of the locomotive and 
tender was 130 tons. On the 1.4% grade the resistance 
of the locomotive would be that due to (121% X 130) = 157 
rating tons. Subtracting this from 922, we have 765 
rating tons behind the locomotive. On the basis that the 
live load is twice the tare, the actual weight of cars with 
their loading would equal 

X 765 = 715 tons. 



2+1.21 



Since | of this weight consists of live load, the actual 
weight of live load carried in one train behind such an 
engine up the 1.4% grade is 477 tons. But, since we are 
assuming that these cars are loaded to the limit of their 
capacity, or at least to the same ratio of that limit, we 
will consider 715 tons as the total weight for both grades 
of the freight and of the cars which carry it. On a 1% 
grade the ratio of tare ton to rating ton is 128%. On 
this grade the locomotive has the equivalent weight of 
(128% X 130) = 166 rating tons. The eight trains, each 



302 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

of which are assumed to have a gross weight for cars and 
live load of 715 tons, will therefore weigh 5720 tons. On 
a 1% grade this will be the equivalent of 

3 
5720 -^TTTi^ = 6254 rating tons. 

The grade and tractive resistance for a rating ton on a 
1% grade equals (20.0 + 2.6), or 22.6 pounds per ton. 
This locomotive at seven miles per hour can therefore 
handle 

28,200 ^ 22.6 = 1248 rating tons. 

Subtracting 166 rating tons for the locomotive, we have 
left 1082 rating tons behind the tender as the capacity of 
one engine. Dividing 6254 by 1082, we have something 
less than 6, which shows that 6254 rating tons could 
be handled by six such engines with a margin of 238 
rating tons. We may therefore say that, as the effect of 
reducing the ruling grade from 1.4% to 1%, the eight 
trains, which are affected by the rate of the ruling grade, 
can now be handled by six engines, and that there will be 
the saving due to the reduction of two trains. If these 
trains were operated 365 days per year, the annual saving 
on the basis of 69 c. per train-mile will be 

2 X $0.69X365 -$503.70 

per mile of length of that division. If the division is 100 
miles long, the annual saving is $50,370. Capitalizing this 
at 5% we have an additional justifiable expenditure of 
$1,007,400. Since this is over three times the computed 
expenditure, which can be readily estimated as the cost 
of effecting this reduction in ruling grade, it would appear 
that the improvement is thoroughly justified, especially 
since future traffic will probably increase rather than 
diminish the value of the improvement. 



CHAPTER XVI. 

PUSHER GRADES. 

202. General principles underlying the use of pusher- 
engines. — Whenever a road is laid out merely with the 
idea of passing through certain predetermined points and 
constructing the road as cheaply as possible, the usual 
result is that there will be a great variety of grades differ- 
ing by small amounts from a level up to the actual maxi- 
mum. In such cases it will usually happen that the term 
'' ruling grade" will apply to only one or two grades along 
the entire length of the road. The length and weight of 
heavy trains will therefore be limited by these ruling grades, 
as already explained in the previous chapter. The obvious 
policy in such cases is to cut down these heaviest grades 
until some limit is reached, at which these heavy grades 
are so numerous and so long that any further reduc- 
tion is financially, if not physically, impossible. The 
economics of such reduction of the ruhng grade has already 
been considered in a previous chapter. It frequently 
happens that there are one or two grades along the line 
on which the tractive resistance is nearly, if not quite, 
twice the tractive resistance of any other grades on the 
line. In such cases the adoption of pusher grades becomes 
economical. If by using assistant engines to assist the 
heaviest trains over one or two steep grades, we are actu- 
ally able to double the length or weight of our freight- 
trains, there is evidently an enormous saving, even though 

303 



304 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

it requires the services of pusher-engines which are used 
for no other purpose. 

203. Numerical illustration of the general principle. — 
In the following illustration the refinements regardirg the 
hauling capacity of locomotives, as determined by rating 
tons, have been ignored. Assume that at one point on a 
road there is a grade of 1.9%, which is five miles long. 
Assume that all other grades are less than 0.92%. Assum- 
ing that all trains are to be operated by one engine through- 
out that division, the net capacity of a consolidation 
engine, weighing 107 tons, with 53 tons on the drivers, 4% 
adhesion, and six pounds per ton for normal resistance, 
will be 435 tons on the 1.9% grade. This is therefore the 
maximum net train-load allowable with that type of 
engine. Assume that this 1.9% grade has a length of 
five miles, and that the whole division is 100 miles long. 
By using pusher-engines on this five-mile grade the net 
train-load can be doubled. These 870 tons can also be 
hauled by one engine up the 0.92% grades. Making a 
rough comparison, which is free from details and allow- 
ances, we may say 

(a) Ten trains per day over a 100-mile division hauling 
435 tons net per train will require 1000 engine-miles per 
day, which will haul 4350 net tons. 

(6) Utilizing pusher-engines on the steep grade, the 
same tonnage of 4350 tons may be handled in five trains of 
870 tons each behind the locomotive. The engine mileage 
will be 5X100 miles of the through-engines plus 2x5X5 
pusher-engine miles, which makes a total of 550 engine- 
miles per day, instead of 1000, to handle a given traffic. 

The advantages of this method are numerous. (1) 
There is not only a large saving in the number of engine- 
miles, but it may even mean a saving in the number of 
locomotives, since it may require the purchase and use of 
ten locomotives in place of seven. (2) The through- 



PUSHER GRADES. 305 

engines, which are hauling 870 tons along the easier grades, 
are working more nearly to the limit of their capacity for 
a large part of the distance, and therefore are doing their 
work more economically. The work of overcoming the 
normal track resistances of so many loaded cars over so 
many miles of track, and of elevating so many tons of 
train weight through the differences of elevation of the 
several points of the line, is approximately the same what- 
ever the exact route. If the grades are so made that 
fewer engines, which are working more constantly to 
nearly the limit of their capacity, can accomplish the 
work as well as more engines, which are doing but little 
work for a considerable proportion of the time, the economy 
is very apparent ai d unquestionable. WeUington ex- 
presses it very concisely: ^'It is a truth of the first impor- 
tance that the objection to high gradients is not the work 
which the engines have to do on them, but it is the work 
which they do not do when they thunder over the track 
with a light train behind 'them, from end to end of a 
division, in order that the needed power may be attained 
at a few scattered points where alone it is needed." 

204. Equating through grades and pusher grades. — The 
above problem was purposely chosen with figures in which 
the pusher grade and the through grade were exactly 
balanced or equated. When it has once been decided that 
pusher grades should be used, then the problem of grade 
reduction is modified to the extent of concentrating effort 
and attention on the reduction of grades which may be 
less than the rate of the pusher grade, and to reduce them 
to the limit of the equated through grade. In other words, 
if it is decided to retain the 1.9% pusher grade, any inter- 
mediate grade between 1.9% and 0.92%, such as 1.4%, 
must necessarily be treated in one of four ways: (a) it 
must be reduced to 0.92%: (b) it might be operated as a 
pusher grade; (c) it might be operated as a through grade, 



306 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

which virtually means that all train-loads are reduced to 
the 1.4% basis; (d) a fourth possible method would be to 
use two pusher-engines on the steepest grade, as described 
below. Of course the first method is the proper method 
to adopt, if it can be done with a reasonable expenditure 
of money. The method of pusher grades is only appHcable 
when it is possible to modify the system of grades on the 
road, so that there is an abrupt change from grades which 
are to be operated as pusher grades down to through 
grades which correspond with these pusher grades. 

A somewhat unusual solution of a problem in pusher 
grades is given by the possibihty of using two pusher- 
engines on some grades and one pusher-engine on corre- 
spondingly lower grades. Working out such a method on 
the basis of the engine previously considered, and assum- 
ing that the 1.9% grade is the grade for two pusher-engines, 
we might determine the corresponding grades for one 
pusher and for through engines as f ollow^s : 

Tractive power of three engines^ 106,000X4^X3 = 
71,550 pounds. 

Resistance on 1 .9% grade = 6 + (20 X 1 .9) = 44 lbs. per ton 

71 ,550 -^ 44 = 1626 = gross load in tons. 

1626- (3 X 107) = 1305 = net load in tons. 

1305 +(2X107) = 1519 = gross load on the one-pusher 
grade. 

Tractive power of two engines = 47,700 lbs. 

47,700 -^ 1519 = 31 .40 = possible tractive force in lbs. per 
ton. 

(31.40- 6) -20 = 1.27% = permissible grade for one 
pusher. 

13Q5_I_ 107 = 1412 = gross load on the through grade. 

Tractive power of one engine = 23,850 lbs. 

23,850-^-1412 = 16.89 = possible tractive force in lbs. per 
ton. 

(16.89-6) ^20=0.54% = permissible through grade 



PUSHER GRADES. 



307 



On account of its simplicity the above problem has been 
worked out on the basis that the normal tractive resist- 
ance is uniformly six pounds per ton, and also that the 
normal adhesion of the drivers is ■^%. On the basis of 
these figures the grades for one, two, and three engines are 
precisely as given above. Using other types of engines and 
assuming other values for the resistance and adhesion, the 
relation of these grades will change somewhat, although, 
as shown in the following tabular form, the variation will 
be but slight. 



Table XXX. — Relati'on of One-pusher and Two-pusher Grades 
TO Through Grades, with Variations of the Ratios of Adhe- 
sion AND Normal Resistance. 



Adhesion 
of drivers. 



To 
i 



Resistance 


Load on 


Through 


One-pusher 


per ton. 


drivers. 


grade. 


grade. 


6 lbs. 


53 tons. 


.54% 


1.26% 


7 '' 


53 " 


.54 


1.29 


6 " 


53 '' 


.54 


1.27 


7 " 


53 " 


.54 


1.31 


6 '' 


53 '' 


.54 


1.28 


7 '' 


53 " 


.54 


1.32 



Two-pusher 
grade. 

1.86% 

1.92 

1.90 

1.96 

1.93 

2.00 



The above form shows that increasing the resistance per 
ton and decreasing the adhesion have opposite effects on 
altering the ratios of these grades, and, as a storm would 
increase the resistance and decrease the adhesion, the 
changes in the ratio would be compensated, although the 
absolute reduction in train-load might be considerable. 
Another practical inaccuracy in the above calculations is 
obtained from the fact that the rating tonnage on the 
pusher-engine service is different from that on the through- 
engine service. To determine the effect on the above case, 
let us consider the original problem of using a 1.9% grade 
as a pusher grade using one pusher-engine. Adopting the 
same figures as before of 2.6 pounds as the resistance of a 
rating ton and 9 pounds as the resistance of a ton of tare, 



308 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

we have, on the 1.9% grade, a gravity resistance of 38 
pounds per ton, and therefore a total resistance of 40.6 
pounds per ton for a rating ton. The resistance of a tare 
ton will be 47 pounds; therefore, to change tare tons into 
rating tons for a 1.9% grade, we multiply the tare ton by 
116% (see Table XXI, § 129). Assuming, as before, an 
adhesion of 4®^ of the 53 tons on the drivers, we have a 
tractive force of 23,850 pounds for one engine, or 47,700 
for two engines. Dividing 47,700 by 40.6, w^e have 1175 
rating tons for the whole train. The two engines weigh 
214 tons, which is the equivalent of 248 rating tons. Sub- 
tracting this from 1175, we have 927 rating tons behind the 
two locomotives. Since the required through grade is 
still an unknown quantity, we must solve the problem by 
an assumption of the required through grade in order to 
determine the equivalent number of rating tons for one 
locomotive on the unknown grade. We know from the 
other solution that the through grade will probably be a 
little less than one per cent, but we know that it will 
probably be a little higher than the rate given by the other 
solution, since a locomotive has a higher resistance per ton 
than the average train resistance. The ratio of tare tons 
to rating tons on a one per cent grade is 128%, therefore 
the number of rating tons on the through grade must be 
very nearly 927 + (107 X 1 .28) = 1064 rating tons. Dividing 
this into 23,850, the tractive power of one locomotive, we 
have 22.40 the total tractive resistance for one rating ton. 
Subtracting 2.6, we have 19.8, which is the grade resistance 
of a 0.99% grade. This value is somewhat higher than the 
0.92% grade previously worked out, as was to have been 
expected. It should be noted, however, that even this 
value depends on the constants, 2.6 pounds for the resist- 
ance of a rating ton and 9 pounds for the resistance of a 
tare ton, as deduced from Dennis's experiments. If the 
solution is worked out on the basis of other values, the re- 



PUSHER GRADES. 309 

suits will probably be somewhat different. On the other 
hand, it is somewhat encouraging that, in spite of the radi- 
cal difference in the methods used, the difference in the 
final results are as small as given above. When separate 
methods give results which agree to a few hundredths of 
one per cent in the rate of the grade, we may consider that 
either are sufficiently accurate for practical use. In view 
of the variations in train resistance and the uncertainties 
of the relation between the resistance for a rating ton and 
the resistance of a tare ton, no table that can be devised 
will be accurate for all conditions. In Table XXXI is 
given the corresponding pusher grades for one- and two- 
pusher, for the same not load behind the locomotive for 
various through grades. These have been v/orked out for 
track resistance of six and eight pounds. The table 
is valuable in that it affords a very ready comparison 
of the relative rates of grade under the conditions named. 
On account of the extra resistance of the extra locomotive, 
the pusher grades are probably a few hundredths of one 
per cent too high, and a corresponding allowance should 
be made. As an illustration of the use of the table, let 
us answer the question of the permissible pusher grade 
when the through grade has already been estabished at 
1.24%. If the road-bed is in good condition, we will 
assume the lower rate of track resistance or six pounds 
per ton. We will then interpolate between 2.34 and 2.50, 
and obtain 2.40% as the corresponding pusher grade. For 
the reason stated above, we should probably cut this down 
to about 2.3%. 

As another illustration, if a road has a few grades of 
1.8% which are not of excessive length and yet which 
cannot be materially reduced except at excessive cost, we 
may consider the question of operating these few grades as 
pusher grades, assuming that all through grades can be 
reduced to the corresponding through-grade limit. Assum- 



310 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

ing again a track resistance of six pounds and interpolating 
for 1.8% for one pusher, we have the corresponding through 
grade of 0.86%. For the same reason as before, this 
should probably be increased to at least 0.90% to obtain 
the correct balance. The question then is transformed 
into the possibility of reducing all grades which are not 
to be operated as pusher grades, so that none are above 
the limit of 0.90%. If the road under consideration is 
already in operation, a closer value may be obtained by 
considering the actual capabilities of the locomotives 
employed and the track resistance as it actually exists. 
For preliminary calculations the above figures are prob- 
ably sufficiently accurate. It may be noted from Table 
XXXI that when the track resistance is increased from 
six to eight pounds per ton, the pusher grade correspond- 
ing to any through grade is increased. This is due 
to the fact that the net load which may be hauled on the 
through grade is considerably less, so much less than on the 
through grade that a larger part of the adhesion is avail- 
able to overcome grade resistance. 

205. Method of operation of pusher grades. — Much of 
the economy in the operation of pusher grades depends on 
the method of operation, which in turn depends on the 
method of their construction. When it is decided that 
pusher grades are necessary, the ideal method of con- 
struction is to concentrate the steep grades into one con- 
tinuous rise. A turnout must be located very near the 
upper and lower ends of each pusher grade, so that the 
pusher-engine may be switched on and off the main track 
with a minimum of useless running. But the ideal arrange- 
ment of a continuous grade is not always practicable. It 
sometimes becomes necessary to lay out a pusher grade for 
a length of perhaps three or four miles, and then, after a 
mile or two of comparatively level ttack, another pusher 
grade several miles in length must be added. It will 



PUSHER GRADES. 



311 



Table XXXI. — Balanced Grades for One, Two, and Three 
Engines. 

Basis. — Through- and pusher-engines ahke; consolidation type; 
total weight, 107 tons; weight on drivers, 53 tons; adhesion, 5%, giving 
a tractive force for each engine of 23,850 lbs,; normal track resistance, 
6 and 8 lbs. per ton. 





Track resistance, 6 lbs 


Track resistance, i 


?lbs. 


Through 
grade, 




Corresponding 




Corresponding 


Net load 


pusher grade for 


Net load 


pusher grade for 


for one 


same ne load. 


for one 


same net load. 




engine in 






engine in 








tons (2000 






tons (2000 








lbs). 


One 


Two 


lbs.). 


One 


Two 






pusher. 


pushers. 




pusher. 


pushers. 


Level. 


3868 tons 


0.28% 


0.55% 


2874 tons 


0.37% 


0.72% 


0.10% 


2874 ' ' 


0.47 


0.82 


2278 '' 


0.56 


0.98 


0.20 


2278 '' 


0.66 


1.08 


1880 " 


0.74 


1.23 


0.30 


1880 " 


0.84 


1.33 


1596 '' 


0.92 


1.47 


0.40 


1596 " 


1.02 


1.57 


1384 " 


1.09 


1.70 


0.50 


1384 " 


1.19 


1.80 


1218 " 


1.27 


1.92 


0.60 


1218 " 


1.37 


2.02 


1085 " 


1.44 


2.14 


0.70 


1085 " 


1.54 


2.24 


977 " 


1.60 


2.36 


0.80 


977 " 


1.70 


2.46 


887 '' 


1.77 


2.56 


0.90 


887 '' 


1.87 


2.66 


810 '' 


1.93 


2.76 


1.00 


810 '' 


2.03 


2.86 


745 '' 


2.09 


2.96 


1.10 


745 '' 


2.19 


3.06 


688 '' 


2.24 


3.15 


1.20 


688 " 


2.34 


3.25 


638 '' 


2.40 


3.33 


1.30 


638 " 


2.50 


3.43 


594 '' 


2.55 


3.51 


1.40 


594 " 


2.65 


3.61 


555 " 


2.70 


3.68 


1.50 


555 " 


2.80 


3.78 


521 '' 


2.85 


3.85 


1.60 


521 '' 


2.95 


3.95 


489 '' 


2.99 


4.02 


1.70 


489 " 


3.09 


4.12 


461 '' 


3.13 


4.17 


1.80 


461 '' 


3.23 


4.27 


435 '' 


3.27 


4.33 


1.90 


435 " 


3.37 


4.43 


411 " 


3.42 


4.49 


2.00 


411 " 


3.52 


4.59 


390 '' 


3.55 


4.63 


2.10 


390 " 


3.65 


4.73 


370 " 


3.68 


4.78 


2.20 


370 '' 


3.78 


4.88 


352 " 


3.81 


4.92 


2.30 


352 '' 


3.91 


5.02 


335 '' 


3.94 


5.05 


2.40 


335 " 


4.04 


5.15 


319 " 


4.07 


5.19 


2.50 


319 " 


4.17 


5.29 


304 " 


4.20 


5.32 



usually be more economical to operate the entire distance 
as a continuous pusher grade, in spite of the fact that for 
a mile or two the pusher-engine is utterly unnecessary. It 



312 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

would be very difficult to so arrange the schedule of trains 
that each section of such a pusher grade could be operated 
separately with separate engines and keep the engines 
continuously employed. Economy in pusher-engine ser- 
vice demands that each pusher-engine shall be working as 
nearly continuously as possible. On account of the great 
loss of economy that occurs when two sections of a pusher 
grade are separated by a mile or two of comparatively level 
track, the engineer can profitably expend considerable 
study and even survejdng, by his corps of men, in the 
endeavor to so modify the line that the total required 
difference of elevation can be condensed into a single grade. 

It has been demonstrated elsewhere that the loss of 
energy incurred in stopping a heavy train is sufficient to 
run it along a level track for a mile or more. It is there- 
fore desirable to couple and uncouple the pusher-engine 
without stopping the train if it is possible. The pusher- 
engine takes its name from the frequent custom of using 
the assistant engine literally as a pusher behind a freight- 
train, which enables it to accomplish its work without 
stopping the freight-train either at the top or bottom of 
the grade. For passenger service the assistant engine is 
always coupled ahead of the through engine, which means 
practically that the train must be stopped when the 
assistant engine is coupled on. The stop at the top of the 
grade is avoided by merely uncoupling the locomotive 
while running, and then running it ahead at increased 
speed on to a flying-switch, where a switchman is located 
so that the passenger-train passes the switch without 
stopping. 

When the traffic of a road is very heavy a pusher grade 
may have several pusher-engines, whose sole duty is to 
serve the trains on that grade. Under such conditions 
they can usually be operated economically. When the 
train service is comparatively light, the pusher-engines are 



PUSHER GRADES. 313 

not SO steadily employed, and the cost of the pusher-engine 
service is proportionally higher for each train assisted. 
If the pusher grade is located very near or even within a 
few miles of a large freight-yard, at which switching- 
engines are constantly employed, a considerable economy 
is frequently possible by employing the pusher-engines 
alternately as switching-engines in the yard and as pusher- 
engines on the pusher grade. 

A still further economy is possible on roads of very light 
traffic, where the use of a pusher-engine would be a luxury. 
On such roads the passenger-trains are usually very short 
and light, and therefore are probably not affected materi- 
ally by the rate of the ruling grade. On such roads also a 
delay of even 50% in the time of hauling a freight-train 
over the road is of comparatively small importance. In 
such cases the road can still be designed on the basis of 
pusher grades. The freight-train can be loaded up to the 
capacity of a single engine on all through grades which 
are less than the pusher grade. The freight- train can then 
be cut in two at the bottom of the pusher grade, and one 
half of the train can be taken up separately. The total 
engine mileage is no greater than with pusher-engine 
service, and in fact may be somewhat less, for reasons 
given in the next section. Almost the only objection is 
that due to the loss in time, and on a road of very light 
traffic this is a small matter. This method should not 
be forgotten, particularly in the design of light-traffic 
roads, since it has all the advantages of enabling a road to 
be designed, if necessary, on a pusher-engine basis, and 
yet if the traffic should ever increase, so that the delay, 
due to this method of operation, becomes objectionable, 
the normal method of pusher-engine service may be 
adopted. The engineer should not forget that the pusher- 
engine method must not be discarded simply because the 
road may not at first have an amount of traffic which 



314 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

would justify the ordinary method of pusher-engine 
service. 

206. Length of a pusher grade. — The actual mileage 
traveled by pusher-engines for each train assisted must 
be something in excess of twice the distance between the 
sidings at the top and bottom of the grade. Usually a 
telegraphic station at both the top and the bottom of the 
grade is at least very convenient if not essential to safe and 
efficient operation. If a regular stopping-place of the road 
is located even a mile or two beyond the top or bottom of 
the pusher grade, it will usually be found advisable, in 
spite of the added mileage, to have the pusher-engine 
service begin at the station. When the assistant engine is 
uncoupled from the train while running, the siding must 
evidently be at some little distance beyond the top of the 
grade, so as to give ample opportunity for the assistant 
engine to run onto a siding and have the switch turned 
before the train passes. All of these allowances add to the 
length of the pusher-engine service, which therefore makes 
it considerably more than the nominal length of the 
pusher-engine grade as taken from a profile of the 
road. 

207. The cost of pusher-engine service. — When we 
analyze the elements of cost, we will find that many of 
them are dependent only on time, while others are depend- 
ent upon mileage. Still others are dependent on both. 
Very much will depend on the constancy of the service, 
and this in turn depends on the train schedule and on a 
variety of local conditions which must be considered for 
each particular case. The effect of a pusher -engine on 
. maintenance of way may be considered to be the same as 
the cost of an additional engine to handle a given traffic, 
as developed in § 86. The same total allowance for the 
expenses of maintenance of way (3.53%) will therefore be 
made. Although the cost of repairs and renewals of 



PUSHER GRADES. 315 

engines is evidently a function of the mileage, and would 
therefore be somewhat less for a pusher-engine which did 
little work than for an engine which was worked to the 
limit of its capacity, yet it is only safe to make the same 
allowance as for other engines. Other items of mainte- 
nance of equipment are evidently to be ignored. The item 
of wages of enginemen will evidently depend upon the 
system employed on the particular road. Whatever the 
precise system the general result is to pay the enginemen 
as much in wages as the average payment for regular ser- 
vice, and therefore the full allowance for Item 21 will be 
made. Similarly we must allow the full cost of the items 
for engine-supplies. While the engine is doing its heavy 
work in climbing up the grade, the consumption of fuel 
and water is certainly greater than the average; but, on 
the'other hand, on the return trip, when the engine is run- 
ning light, it probably runs for a considerable portion of 
the distance actually without steam, and therefore the 
consumption of fuel and water will nearly, if not quite, 
average the consumption for an engine running up and 
down grade along the whole line. That portion of fuel 
consumption which is due to radiation, blowing-off steam, 
and the many other causes previously enumerated, will 
be the same regardless of the work done. We therefore 
allow 100% for all of these items of engine-supplies. In 
general we must add 100% for Items 28 and 29, the cost 
of switchmen and telegraphic service. While there might 
be cases where there would be no actual addition to the 
pay-rolls or the operating expenses on account of these 
items, we are not justified in general in neglecting to add 
the full quota for such service. Collecting these items we 
will have 37.20% of the average cost of a train-mile for 
the cost of each mile-run by the pusher-engine. Using 
the same figure as before, $1.30, for the cost of one train- 
mile, we have 48.36 c. for each mile-run. Again adding, 



316 THE ECONOMICS OF RAILROAD CONSTRUCTION. 



as in § 200, 1.25 c. as interest charge on the cost of the 
pusher-engine, we have 49.61 c. for each mile. 

Table XXXII. — Cost for each Mile of Pusher-engine Service. 



No. 



Items (abbreviated). 



Normal 


Per cent 


average. 


affected. 


10.767 


12.5 


1.422 


50. 


2.948 


50. 


6.538 


100. 


9.607 


100. 


11.542 


100. 


4.110 


100. 


1.875 


100. 



Cost per 
engine- 
mile, 
per cent. 



1 

2 

3 

12 

21 

22-2^ 
28 
29 



Repairs of roadway. , , 

Renewals of rails 

' ' ties. . . . . . 

Repairs of locomotives 

Enginemen 

Engine-supplies 

Switchmen, etc 

Telegraph 



1.35 
.71 
1.47 
6.54 
9.61 
11.54 
4.11 
1.87 

37.20 



2o8 Numerical illustrations of the cost of pusher service. 

— In § 204 we found that a through grade corresponding to 
a 1.9% pusher grade was 0.99%, or, in other words, that 
two engines of equal capacity could handle on a 1 .9% grade 
a train which could be hauled by one engine on a 0.99% 
grade. Suppose that we have a road or division 100 miles 
long, which has a traffic of ten trains per day each way 
which must be assisted by pusher-engines. Two of the 
grades, 5 and 6.5 miles respectively, are against the 
traffic in one direction, and the other grade, with a 
length of 7.5 miles, is against the traffic in the other direc- 
tion. There will therefore be a total of 19 miles of 
pusher-engine grade, on which ten trains per day must 
be assisted. Suppose that these maximum grades have 
been limited by suitable development to 1.9%. Suppose 
that the other grades are less than 1% or a^e so little 
above it that, with a comparatively small expenditure, 
they may be reduced to 1% or to 0.99%. How much 
money could justifiably be spent to accomplish the reduc- 
tion of the other grades to keep them within the Hmit of 



PUSHER GRADES, 317 

0.99%? There will be no object in cutting down these 
intermediate grades, unless by so doing we can double the 
train-load, even though doubling the train-load adds the 
expense of operating the pusher service. If the traffic of 
the road is sufficient for ten trains, such as could be hauled 
with one engine over the 0.99% grades, it will require 
twenty such trains to haul that traffic with one engine over 
1.9% grades. Therefore, utilizing the pusher-engine ser- 
vice will save the operation of ten trains per day each way. 
If this particular division of the road is 100 miles long, 
the annual saving by cutting down the number of trains 
from twenty to ten, computed as in the previous chapter, 
will be 

10X10.69X100X365-= $241,850. 

But this saving is accomplished only by the pusher service, 
which will cost 

10X19X2X49.61 c.X365 = 68,809 per year. 

Capitalizing the net saving $173,041 at 5%, we have 
$3,460,820, which represents the amount which might jus- 
tifiably be spent in reducing all grades except the three 
pusher grades down to the hmit of 0.99%. The above 
estimate may need to be modified somewhat as to the cost 
of the pusher service. If these three pusher grades were 
so widely separated that each must be operated independ- 
ently, then the pusher-engine mileage per day for the 
three grades would be 100, 130, and 150 miles respec- 
tively. Unless the schedules were favorably arranged for 
the pusher-engine service, it is quite possible that one 
engine might not be able to do the entire work on each of 
the grades. Freight-trains which require pusher-engine 
help usually move at a very low speed, probably less than 
15 miles per hour, and at times not more than 10 mileg 



318 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

per hour. One hundred and fifty miles per day for a 
pusher-engine impUes a very well-arranged schedule, and 
therefore two pusher-engines might be needed instead of 
one. This would add considerably to the cost of the 
pusher-engine service. The cost of reducing these grades 
is a quantity which can be readily computed with all 
desired accuracy, therefore we can usually determine by 
an investigation like the above whether the plan of using 
a pusher-engine service is desirable, since the cost of 
reducing the grades might be very much less than the 
computed capitalization. In that case it would show that 
it would probably be justifiable to adopt such a policy 
and that any allowable inaccuracy in the method of esti- 
mating the difference in operating expenses would not 
alter the final result. On the other hand, if the cost of 
reducing the grades is materially greater than the capital- 
ized value, the proper method is again clearly indicated. 
"VAHien the two values are substantially equal, it shows that 
there is but little choice, and that the choice must probably 
be determined by the facility with which the money for 
the improvement can be obtained. In applying the above 
methods to any particular case, the values given above 
should be closely studied and revised to agree as nearly as 
possible with the local conditions. The value of the cost 
of a pusher-engine mile given above is to be considered 
as merely illustrative of what the cost will be under some 
conditions. Under other conditions the variation will be 
considerable, and a value which will correspond with the 
local conditions should be determined. 



CHAPTER XVII. 

BALANCING GRADES FOR UNEQUAL TRAFFIC. 

209. Nature of the subject. — In the preceding chapters 
it has been tacitly impUed that the extent of the traffic 
in the two directions is equal, and that it is just as desir- 
able to obtain a low grade in one direction as in the other. 
But it frequently happens that the freight traffic in one 
direction is far greater than the freight traffic in the oppo- 
site direction. Even on the main trunk lines running east 
and west, the east-bound ton-mileage has at times amounted 
to four or five times the west-bound ton-mileage. Be- 
tween the years 1851 and 1885 the east-bound ton-mileage 
on the Pennsylvania Railroad averaged 3.7 times the 
west-bound ton-mileage. As an actual consequence, the 
west-bound freight-trains consisted very largely of 
^^ empties." As another corollary, a locomotive which 
could haul a certain number of loaded cars up a grade of 
0.6%, which was against the east-bound traffic, could just 
as easily haul such cars as were loaded, together with the 
empties, which must be returned, up a considerably steeper 
grade, say 1.0%. Under such conditions there is little 
or no object (from the ruling-grade standpoint) of making 
the grade against the west-bound traffic any less than 1% 
when the east-bound traffic is as steep as 0.6%. The two 
grades, 0.6 and 1.0, have been selected offhand as two 
grades which might balance each other under certain 

319 



320 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

conditions of relative traffic in the two directions. They 
illustrate the principle involved that the ruling grades in 
opposite directions should not necessarily be equal, but 
should probably be made unequal. It now remains to 
determine what should be the relation between the ruling 
grades in the two directions on any given road. 

210. Illustrations in the balancing of grades. — This sub- 
ject is one that chiefly concerns the great trunk lines of 
the country, which are constructed almost regardless of 
cost and at grades which are reduced to a low figure by 
a great expenditure of money. A very large number of 
railroads, especially branch lines which run from a main 
road up into the mountains, have one terminus much 
higher than the other, are laid out largely as ^'surface 
lines," and are therefore laid on such grades as can be 
obtained with a minimum of constructive work. On such 
a road the heavy grades may be almost entirely in one 
direction, which may or may not be against the heavy 
traffic. 

Unless a road is of such importance that it can be largely 
rebuilt after its original construction, in order to correct 
the errors and deficiencies of the original work, we must 
consider the original location as a finality. It is frequently 
impossible to predict, with any great accuracy, what the 
traffic of the road will be, and especially that the traffic 
in one direction will be materially greater by any definite 
percentage than that in the other. The engineer is there- 
fore seldom justified in attempting to make precise cal- 
culations of this sort previous to the construction of a new 
road. 

211. Principles on which the theoretical balance must be 
computed. — A little thought will show the truth of the 
following statements. First, the number of locomotives 
and passenger-cars running in each direction is necessarily 
equal. Second, the number of passengers carried in 



BALANCING GRADES FOR UNEQAL TRAFFIC, 321 

opposite directions is practically equal. Even if we allow 
that there is a considerable immigrant traffic which in- 
creases slightly the load of passengers carried, it is useless 
to base any calculations on this, since the ratio of live load 
to dead load in passenger-cars is so very small that such 
a slight difference in the number of passengers carried in 
opposite directions as may exist can have absolutely no 
effect on the proper rate of grade. Third, empty cars have 
a greater resistance per ton than loaded cars; therefore, in 
computing the hauling capacity of a locomotive hauling so 
many tons of '^empties," a larger figure must be used for 
the ordinary tractive resistances. This fact, so far as it 
goes, tends to equalize the differences in the two grades 
which might otherwise be computed. Fourth, owing to 
greater or less imperfections of management, a small per- 
centage of cars will run empty or partly full in the direction 
of the greatest traffic. Fifth, freight having great bulk 
and weight (such as grain, lumber, coal, etc.) runs from 
the rural districts to the cities and manufacturing dis- 
tricts. Sixth, freight from manufacturing districts, although 
it pays comparatively high freight-rates and is actually 
more profitable to handle, weighs far less, and occupies 
less bulk. Seventh, changes in traffic conditions which are 
more or less permanent will alter the direction of the 
hauling of bulk freight. For instance, a farming district 
which is largely a dairying country frequently will not 
raise as much feed (hay and grain) as is needed to feed the 
cattle, and we have the apparent paradox of importing 
grain and feed into a farming country. Eighth, a change 
in the character of the country may permanently alter the 
ratio of the freight tonnage in the two directions. Such 
changes are already discernible in the traffic of the east 
and west lines and also in the north and south lines. The 
discovery of extensive coal-fields in the western part of the 
United States has largely changed the direction of the 



322 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

movement of this class of bulk freight. The exhaustion 
of supplies of timber in one section and the development 
of that industry in another has also had material influ- 
ence in changing the relative flow of traflfic. The develop- 
ment of the coal and iron industries in the South has 
largely changed the relative traffic flow in north and 
south lines. 

212. Numerical illustration. — Assuming the same figures 
already considered in Chapter X, we will consider that the 
grade against the heaviest traffic and for fully loaded 
trains is 1%. The grade and tractive resistance for a 
rating ton on this grade is 22.6 pounds per ton. If the 
locomotive has a tractive power of 23,290 pounds, it can 
handle 1248 gross rating tons. The actual weight of the 
locomotive and tender is 130 tons; multiplying this by 
128% for the 1% grade, we have 166 rating tons for the 
locomotive which leaves 1182 rating tons behind the 
tender. If the fully loaded trains have a live load equal 
to twice the weight of the cars, their actual tonnage will 

3 
be ^ — -—^X 1182 = 1081 tons. This means that !he cars 

weigh 360 tons and the freight 721 tons. Assume that 

the total live load carried in the opposite direction is but 

J of the above, we would then have 360 tons of cars and 

240 tons of freight, which will aggregate 600 tons. To 

determine the rating tons corresponding to 600 actual 

tons of loading, we must make first a trial estimate of the 

grade in order to determine the value of a rating ton on 

that grade. We will assume as a trial that the grade is 

1.6%. At this grade the ratio of a tare ton to a rating 

ton is 119%. Since the five load is J of a nominal full 

load, which means that it is f the weight of the cars, to 

reduce 600 actual tons to rating tons at 1.6% we must 

-+1 
divide 600 by jxTTq' which ec^uals 668 rating tons. 
3 + i.iy 



BALANCIxNG GRADES FOR UNEQUAL TRAFFIC, 323 

But on a 1.6% grade the 130-ton locomotive will have the 
equivalent weight of 155 rating tons. Adding this to 668 
rating tons for the load behind the tender, we have 823 
rating tons as the total weight of the train. If we divide 
the total tractive power 28,200 by 34.8, the tractive 
resistance of a rating ton on a 1.6% grade, we would have 
811 as the total capacity in rating tons of the locomotive 
on the 1.6% grade. This agrees fairly well with 823, but 
it proves that the trial rate of grade, 1.6%, is a little too 
high. If we were to carry through another trial calcula- 
tion on the basis of 1.5%, we would find a far greater dis- 
crepancy in the other direction. Considering that our 
assumption of the probable weight of the loading in the 
direction of light traffic is at its best a gross approxima- 
tion, any over-refinement in these calculations is a mere 
waste of time. We may therefore say that, under the above 
conditions, a grade of 1% against the heaviest traffic will 
give as much resistance and require as much work of the 
engines as a grade of 1.6% against the assumed lighter 
traffic. 

213. Reliability of calculations of this nature. — As 
before intimated, this is not a question which will ordina- 
rily concern the engineer of a light-traffic, cross-country 
road. The practical difficulty of predicting the relative 
amount of traffic on a road before it is constructed, and 
the probabihty that such figures, no matter how correct 
they might be in the early history of the road, will be 
permanently altered in the course of 20 or 50 years, means 
that very little reliability can be placed on such computa- 
tions except in a general way. The great east and west 
trunk lines, although they find that there are fluctuations 
in the relative amounts of traffic, have also discovered that, 
in a rough way, the east-bound traffic is permanently far 
greater than the west-bound traffic. The Pennsylvania 
Railroad, in the course of the carefully developed recon- 



324 THE ECONOMICS OF RAILROAD CONSTRUCTION. 

struction of their line and the building of a low-grade line 
between Philadelphia and Pittsburg, have kept this prin- 
ciple in mind, and have uniformly designed the ruling 
grade against the east-bound traffic at a considerably lower 
figure than that against the west-bound traffic. The 
Canadian Pacific has already begun extensive reconstruc- 
tion of their line in order to follow this same principle. 
In an extreme case pusher grades may be used to accom- 
plish the same object, but this does not alter the pjinciple 
involved. A pusher grade should always be considered as 
a special case of a ruling grade of a little over one-half the 
rate which is operated in a special way, and the above 
principle is one which applies to the relative rate of the 
ruling grade. Although the engineer of a light-traffic road 
may not find it justifiable to spend any added amount of 
money to follow this principle, he should keep it in mind 
and endeavor to so design his ruling grades to conform 
to this principle, if it may be done with little, if any, added 
expenditure. 



INDEX. 

Numbers refer to sections except where specificaUy marked pages (p.) . 

Acceleration curves 131 

Acceleration of trains, force required 120 

Accidents, cost as affected by curvature 175 

danger of, due to curvature 160 

justification of unusual expenditure to avoid them .... 5 

probability during any one railroad trip 5 

proportion for which railroads are responsible 5 

total number of killed and injured 5 

Additional cost of operating a given freight tonnage with four en- 
gines on heavy ruling grades instead of with three 

engines on lighter grades — Table XXIX p. 300 

cost of operating a given freight tonnage with four light 

engines instead of three heavier engines — Table XII p. 135 

Adhesion of locomotive driving-wheels. . 126, 130 

Air-brakes — see Brakes. 

Air resistance — see Atmospheric resistance. 

American type of locomotives, cost 83 

Aspinall's formula for train resistance 121 

Assistant engines— see Pusher engines and Pusher grades. 

Atmospheric resistance 115 

Automatic air-brakes, extent of use 94 

couplers, extent of use 95 

Average cost per train -mile for the whole United States — 1890- 

1904— Table VII p. 85 

Averages, statistical, danger in indiscriminate use 6 

Balanced grades for one, two, and three engines — Table XXXI . . p. 311 
BALANCING GRADES FOR UNEQUAL TRAFFIC— Chap. XVII. 

determination of theoretical balance 211 

nature of the subject 209 

numerical illustration 212 

325 



326 INDEX. 

Baldwin Locomotive Works' formula for train resistance. 121 

Barnes's formula for train resistance 121 

Boiler, limitation of steaming capacity 12(5, 127 

Bond, convertible, financial character 13 

equipment trust, financial character 13 

income, financial character. 13 

Bonds, interest, average rate 15 

interest, percentage of defaulted interest 15 

limitation of bonded debt 8 

power of bondholders to demand foreclosure sale 13 

Brake resistances 119 

Brakes, air- or train-, extent of use 94 

Bridges and culverts, cost of renewals and repairs 55 

as affected by changes in alinement and 

operating conditions. ... 86, 138, 164, 186 
Buildings and fixtures, cost of renewals and repairs 56 

CAPITALIZATION— Chap. III. 

minimum required by State laws 10 

railroad, practical limitations 19 

principles governing amount 20 

Capital, railroad, growth for decennial periods 2 

per inhabitant 1 

per line of mile 1 

Car construction, economics of 90-98 

Car-mileage, cost 69 

Cars, capacity of various types 91 

causes of deterioration 139 

cost of renewals and repairs 59, 139 

as affected by changes in aline- 
ment 87, 139, 170, 190, 199 

draft-gear 96-98 

high capacity, economy 93 

ratio of live load to dead load 92 

Car-wheels, rotary kinetic energy of 120, 124 

Charters, special privileges granted 9 

Chemical treatment of ties 107 

economics of 108 

Classification of operating expenses 49 

of traffic 151 

Coal — see Fuel. 

Coaling stations, cost of operation 78 

Commodity rates, special, justification 31 



INDEX. 327 

5aiparative cost of various sizes of standard gauge simple locomo- 
tives— Table XI p. 127 

value of cross-ties of different materials 108 

Condemnation proceedings, regulations regarding them 11 

Compensation for curvature 179, 180 

meaning and necessity 179 

rate 180 

Competition, direct, effect on rates 29 

indirect, effect on rates 30 

Concrete ties, economics of 108 

Conducting transportation, cost of 61-71 

cost of as affected by changes in dis- 
tance 140-149 

as affected by curvature 172-175 

minor grades 191 

ruling grades 200 

Consolidation locomotives, cost of 83 

weight and tractive power 196 

of railroad corporations 37 

Constructive tnileage, as used in payment of enginemen's wages. . 77 

Cost, comparative, of various types of locomotives 83 

for each mile of pusher-engine service — Table XXXII. . . .p. 316 

of curvature, per degree of central angle 176 

of handling a given traffic wdth one less train 85-88 

of maintenance and operation of locomotives, 1894-1904 — 

Table X p. 110 

of one additional mile of distance per daily train per year . . 150 
of one additional foot of distance per daily train per year, . . 150 

of pusher-engine service 207 

numerical illustration 208 

of renewals of rails 53 

of ties 54-104 

of repairs and renewals of bridges and culverts 55 

of fences, road-crossings and cattle- 
guards 56 

of freight-cars 59 

of locomotives 58 

of passenger-cars 59 

of repairs of roadway 52 

of tie renewals, annual 104 

of ties, actual, as distinguished from first cost 106 

per train-mile, average for United States 50 

total, of power, by the use of locomotives 74 



328 INDEX. 

Creosoted ties, economics of 107, 108 

Cross-ties — see Ties. 

Culverts, cost of renewals and repairs 55 

■ CURVATURE— Chap. XIII. 

effect in limiting length of trains 162 

the use of heavy engines 162 

on speed of trains 161 

on traffic 161 

limitations for maximum 181 

Curve resistance 118 

per degree of curve 118 

Curves, cost per daily train per year of one degree of central angle . 176 

effect on rail wear 100-103 

Cushing, W. C, author of demonstration of comparative value of 

cross-ties of different materials 108 

Damages to persons and property, cost 70 

Demurrage charges on detained cars 69 

Dennis, A. C, author of demonstration on momentum diagrams 

and tonnage ratings 128, 133 

Determination of coordinates of velocity-distance curves for one 

type of locomotive — Table XXII p, 218 

Discrimination in rates, effect on receipts and profits 30 

DISTANCE— Chap. XIII. 

compensation to cost of increased distance 153-154 

effect of change in the length of the home road on its 
receipts from through-compet- 
itive traffic 153, 154 

on business done 158 

effect on operating expenses 138-150 

justification of decrease to save time 157 

relation to rates and expenses 135 

Distribution of the cost of engine repairs to its various contributing 

causes— Table XXIII p. 232 

Dividends on railroad stocks 14 

railroad, variation due to variation in business 18 

Docks and wharves, cost of repairs and renewals 56 

Dowels, use in ties 112 

Draft-gear 96-98 

friction 98 

spring 97 

Dynamometer tests for train resistance 123 

Earnings, railroad, estimation by comparison 43 

detailed computation 44 



INDEX. 32^ 

Earnings, railroad, gross amount from various sources 17 

per capita 40 

per mile of road for large and small roads. ... 4L 

per mile of road in various groups 40 

per train-mile for large and small roads 41 

ECONOMICS OF CAR CONSTRUCTION.— Chap. VIII. 

Economics of change in distance, general conclusions 156 

heavy locomotives 84-89 

high capacity of cars 93 

rails 99-103 

the locomotive 74-83 

ties 104-112 

railroad, justification of methods of computation . 73, 178, 193 

Economy of pusher grades 203 

Effect of curvature on operating expenses 163-177 

of distance on receipts 151-155 

on operating expenses of 26.4 feet of rise and fall — Table 

XXVI p. 286 

of changes in curvature — Table XXV 

p. 263 
of great and small changes in dis- 
tance — Table. XXIV p. 239 

Elimination of curvature, financial value I77 

of distance, numerical illustration of financial value. . 177 

Eminent domain, right of, inherent in railroad corporations H 

Employees, railroad, proportion of total population 4 

total number in railroad service 4 

wages paid 4, 62, 77 

Engine- and roundhouse-men, wages 62, 77 

Enginemen, methods of payment of wages 62, 77 

English locomotives, mileage life 75 

Estimates on economics, reliability 73^ 178, 193 

ESTIMATION OF VOLUME OF TRAFFIC— Chap. V. 

Expenditure of money for railroad purposes, general principles. . 19, 20 

Extra business, cost of handling 28 

Federal control, constitutional basis 33 

of rates 33-37 

Fixed charges, character 15 

ratio to total disbursements 13, 18 

Formula for accelerated motion 131 

tractive force. . . : 126 

resistance 117 



330 INDEX. 

Formulae for inertia resistance 120 

train resistance 121 

Freight rates on bulky freight 32 

rational basis of determination 28 

traffic, average haul per ton in miles 45 

number of tons carried one mile per mile of 

Hne 45 

in a train 45 

Friction draft-gear C8 

journal, of axles 116 

rolling, of wheels 116 

Fuel for locomotives, cost 63, 78 

for handUng coal at coaling stations. ... 78 
of, as affected bv changes in alinement 

88, 142, 200 

relative value of various kinds and grades . . 78 

Tunded debt, ratio to total capitalization 13, 18 

Grade — see Minor Grades, Pusher Grades, Momentum Grades, 
R.uhng Grades, Balancing of grades for unequal traffic. 

Grade resistance 117 

virtual 125 

use, value, and misuse 126, 127 

Grades, accelerated motion of trains on 120, 124, 127, 131 

distinction between minor and ruling 182 

minor — see Minor grades, 
pusher — see Pusher grades, 
ruling — see Ruling grades. 
Gross and per-capita railroad earnings, whole United States — 

Table III p. 68 

Gross earnings per mile of road and per train-mile for great and 

smafi roads (1904)— Table V p. 71 

Henderson, G. R., tonnage-rating formula 131 

Hitt, Rodney, economics of high-capacity cars 93 

Humps in a grade, financial value of removal 186-193 

operation of a train over them by means of momentum. . . 127 

Impurities in water for boiler use 79 

Incorporators, number required in various States 10 

Inertia resistance 120 

Injuries to persons, cost 70 

Interstate Commerce Act 34 



INDEX. 331 

Journal friction of axles 116 

Kinetic energy of trains 124-127 

Law of increasing returns 28 

Laws, general railroad 10 

in State of New York 11 

of journal friction 116 

Life (in months) of 100-lb. rails— Main line, P. R. R.— Table XIV, p. 156 
of rails on mountain curves — A. T. & S. F. Rwy. — 

Table XIII p. 155 

Life of locomotives 75 

Limitations of curvature 181 

Local traffic, definition and distinction from through traffic 151 

Location of terminals and stations Lt a distance from business 

centers, effect 46, 47 

Locomotives, cost of fuel 63 

of repairs and renewals 58 

of various types 83 

heavy, use on very sharp curvature 162 

heavy vs. Hght 84-89 

internal resistances 114 

hfe of 75 

repairs and renewals, as affected by changes in 

alinement 87, 139, 169, 190, 199, 207 

tonnage rating 129 

types, as affected by sharp curvature 162 

water-supply 64 

Long-and-short-haul clause, Interstate Commerce Act 34 

Loss in traffic due to lack of facihties 46-48 

Maintenance of equipment, as affected by changes in curvature . 168-171 

distance 139 

minor grades 190 

ruhng grades 199 

pusher-engines 207 

weight of engines 87 

cost '. 57-60 

Maintenance of Way, as affected by changes in curvature 164-167 

distance 138 

minor grades 186-189 

weight of engines 86 

cost 52-56 

and Structures, discussion of items 52-56 



332 INDEX. 

-Map showing Interstate Commerce Commission division of railroads 

into groups 13 

Marine equipment, cost of repairs and renewals 60 

Maximum train-load on any grade 196 

Metal ties, economics of 104-108 

JMileage, car • 69 

life of locomotives 75 

railroad, annual growth in- the United States 1 

per 100 square miles of territory 39 

total in the United States 1 

Miles of line per 100 square miles of territory 1 

MINOR GRADES.— Chap. XIV. 

basis of cost 183 

classification 185 

distinctive character 182 

effect on operating expenses 186-193 

estimate of cost of one foot of change of elevation 192 
numerical illustration of financial value of re- 
duction 193 

Mogul locomotives, cost and dimensions 83 

Momentum diagrams and tonnage ratings 128-134 

MOMENTUM GRADES.— Chap. XI. 

Monopoly in railroad business, possible extent 48 

MOTIVE POWER.— Chap. VII. 

National wealth and railway capital — Table II p. 10 

^Non-competitive traffic, extent of monopoly 48 

Uorthern Pacific Railroad, rail-wear statistics 101-103 

J^umerical illustration of balancing grades for unequal traffic. . . . 212 

of the cost of pusher service 208 

of ratios of corresponding pusher and 

through grades 204 

Objections to curvature 159 

Oil, use for fuel for locomotives 78 

OPERATING EXPENSES.— Chap. VI. 

•Operating Expenses, classification 51 

per train-mile, as affected by changes in 

curvature 163-177 

per train-mile, as affected by changes in 

distance 138-150 

per train-mile, as affected by minor 

grades 188-192 



INDEX. 333 

Operating Expenses, per train-mile, as affected by ruling grades 199, 200 
per train-mile, as affected by weight of 

engine 85-88 

per train-mile, fourfold distribution 50 

method of dist bution 50 

on large and small roads, 

1904— Table VIII ..p. 86 

uniformity 50 

Operation of trains, effect of curvature on 162 

ORGANIZATION OF RAILROADS.— Chap. II. 

Oscillatory and concussive velocity resistances 115 

Passenger-cars, cost of repairs and renewals 59 

-miles, total per year 3 

traffic, average journey per passenger in miles 45 

average number in train in various groups. ..... 45 

number of passengers carried one mile per mile 

of line 45 

proportion of earnings to total in various groups . 45 

Pooling of railroad receipts 35 

Pools, money 35 

traffic. . 35 

Profit and loss, dependence on variations in business done 18 

small margin between 17 

Projects, railroad, economic justification of 7 

Property, private, appropriation of by railroads 10 

railroad, basis of ownership 8 

Public service of railways, by groups (1900) — Table VI p. 76 

ratios of various kinds 3 

Purification of water-supply for boiler use 80 

Pusher-engine service, cost 207 

PUSHER GRADES.— Chap. XVI. 

length 206 

method of operation 205 

principles underlying use 202, 203 

relation to corresponding through grades .... 204 

Rail renewals, as affected by changes in distance 138 

curvature 166 

minor grades 188 

weight of engines 86 

Rails, cost of renewals 53 



334 INDEX. 

Rails, minimum weight permitted by law 11 

Rail wear on curves — Northern Pacific R. R., Minnesota Div. — 

Table XIX p 162 

— Northern Pacific R. R., Pacific Div.— 

Table XVIII p. 161 

per degree of curve 103 

on tangents — Northern Pacific R. R. — Table XV p. 157 

relation of rate to the life-history of the rail 102 

statistics 100, 101 

theoretical. 99 

Railroad statistics — Table I p. 9 

Rates, railroad, based on distance, reason 135-137 

basis of determination 28 

limitations 10 

Rating tons, meaning of 129 

Ratio of tare tons to rating tons for various grades — Table XXI . . p. 211 
Relation of one-pusher and two-pusher grades to through grades, 
with variations of the ratios of adhesion and normal 

resistance — Table XXX p. 307 

of radius of curvature and of degree of central angle to 

operating expenses 163 

Renewals of locomotives 58, 75 

Repairs and renewals of bridges and culverts, cost 55 

of freight-cars, cost 59 

of locomotives, cost 58 

as affected by changes in 

operating conditions, 87, 139, 
169, 190, 199 
of passenger-cars, as affected by changes in 

operating conditions. . 87, 139, 170, 190, 1C9 

of passenger-cars, cost 59 

Repairs of locomotives 76 

average cost per engine-mile 76 

per thousand ton-miles 76 

Repairs of roadway 52 

as affected by changes in operating conditions, 

86, 138, 165, 187 

Resistance atmospheric 115 

curve 118 

grade 117 

train, formulae for 121 

Resistances due to brakes 119 

due to inertia 120 



INDEX. 335 

Resistances, internal, to the locomotive 114 

oscillatory and concussive 115 

velocity 115 

Retardation curves 132 

Revenue, gross, distribution of 17 

Rise and fall, technical meaning of 184 

Roadway, cost of repairs 52 

(See also Repairs of roadway.) 

Roller-bearings, advantages and use 116 

Rolling friction of wheels 116 

Rotative kinetic energy of wheels of train 120, 124 

Roundhouse-men, wages paid 62, 77 

RULING GRADES.— Chap. XIV. 

definition. 194 

determination of 195 

numerical illustration of value of reduction. . . 201 

proportion of traffic affected by them 197 

Sags, operation of a train through them by means of momentum . . 127 

Screw-spikes, use in ties Ill 

Searles's formula for train resistance 121 

Service, railroad, value compared with cost 135 

Shop machinery and tQols, cost of repairs and renewals 60 

Slipping of wheels on rails, lateral, effect on rail wear 99 

longitudinal, effect on rail wear 99 

Speed of trains, limited by sharp curvature 161 

relation to tractive adhesion 130 

Spring draft-gear 97 

State control 9-11 , 38 

STATISTICS.— Chap. I. 

of mileage and gross earnings in different sections of 

"he United States (1900)— Table IV p.. 69 

Steel ties, economics of 108 

Stock, dividends on, percentage paying no dividends 14 

per mile of line in various sections of the country 12 

preferred, privileges and limitations 12 

railroad, total for railroads of United States 12 

Summary showing classification of operating expenses for the year 
ending June 30, 1904, and proportion of each class to total 
for the years ending June 30, 1904, to 1895— Table IX. pp. 88-91 

Supplies, miscellaneous, for locomotives, cost 82 

Switching charges 68 

engines, used in pusher-engine service 205 



336 INDEX. 

TABLES. — Numbers refer to pages, not sections. 

I. Railroad statistics 9 

II. National wealth and railway capital 10 

III. Gross and per-capita railroad earnings — whole United 

States 68 

IV. Statistics of mileage and gross earnings in different sec- 

tions of the United States (1900) 69 

V. Gross earnings per mile of road and per train-mile for 

great and small roads (1904) 71 

VI. Public service of railways by groups (1900) 76 

VII. Average cost per train-mile for whole United States — 

1890-1904 85 

VIII. Operating expenses per train-mile on large and smaU 

roads (1904) 86 

IX. Summary showing classification of operating expenses 
for the year ending June 30, 1904, and proportion of 
each class to total for the years ending June 30, 

1904, to 1895 88-91 

X. Cost of maintenance and operation of locomotives, 1894- 

1904 110 

XI. Comparative cost of various sizes of standard-gauge 

simple locomotives 127 

XII. Additional cost of operating a given freight tonnage with 

four light engines instead of three heavier engines. 135 

XIII. Life (in months) of rails on mountain curves 155 

XIV. Life (in months) of 100-pound rails, main line, P. R. R. . 156 
XV. Rail wear on tangents. Northern Pacific R. R 157 

XVI. Yearly wear (in pounds) of outer rails — sharp curves. .. 158 

XVII. Yearly wear (in pounds) of rails on tangents ICO 

XVIII. Rail wear on curves, Northern Pacific R. R., Pac. Div. . 161 
XIX. Rail wear on curves, Northern Pacific R. R., Minn. Div. 162 
XX. Velocity head (representing the kinetic energy) of trains 

moving at various velocities 203 

XXI. Ratio of tare tons to rating tons for various grades. ... 211 
XXII. Determination of ccordinates of velocity-distance curves 

for one type of locomotive 218 

XXIII. Distribution of the cost of engine repairs to its various 

contributing causes 232 

XXIV. Effect on operating expenses of great and small changes 

in distance 239 

XXV. Effect on operating expenses of changes in curvature. . . 263 
_ XXVI. Effect on operating expenses of 26.4 feet of rise and 

fall 286 



INDEX. 337 

TABLES. — Numbers refer to pages, not sections. 
XX VII. Tractive power of various types of standard -gauge loco- 
motives at various rates of adhesion. . 292 

XX VIII. Total train resistance per ton (of 2000 pounds) on 

various grades 294 

XXIX. Additional cost of operating a given freight tonnage 
with four engines on heavy ruling grades instead of 

with three engines on lighter grades 300 

XXX. Relation of one-pusher and two-pusher grades to through 
grades, with variations of the ratios of adhesion and 

normal resistance 307 

XXXI. Balanced grades for one, two, and three engines 311 

XXXII. Cost for each mile of pusher-engine service 316 

Tare ton, meaning of 129 

Taxes, railroad, annual amount paid 16 

average assessment per mile 16 

average rate of taxation. . 16 

method of assessment 16 

Telegraph plant, cost of repairs and renewals 56 

Terminals, effect of location on business 46 

Through rates, method of division between the roads on which 

through traffic is carried 152 

Through traffic, definition 151 

effect of changes in distance on receipts 153 

Tie-plates 109, 110 

economics of 109 

wooden 110 

Tie renewals, as affected by changes in operating conditions.. . 86, 138, 

167, 189 

Ties, actual cost as distinguished from first cost 106 

chemical treatment 107 

cost of renewals 54 

form, economics of 108 

methods of deterioration and failure 105 

protection against wear 109 

use of dowels 112 

use of screw-spikes Ill 

Time, reduction in distance to save 157 

Ton-miles per pound of coal burned in locomotives 78 

Tonnage rating for a given grade and velocity 130 

of locomotives 129-134 

TRACK ECONOMICS.— Chap. IX. 

Tractive power of various types of standard -gauge locomotives at 

various rates of adhesion — Table XXVII p. 292 



338 INDEX. 

Traffic associations 36 

classification of weight 151 

effect of change of distance on 158 

facilities, effect on volume of business 46, 47 

railroad, ''necessary" and ''unnecessary" 48 

Train-brakes — see Brakes. 

Train length, limitation by curvature 162 

load, increase in, financial value of 198 

maximum on any grade 196 

TRAIN RESISTANCE.— Chap. X. 

Train-resistance formulae 121 

results compared 122 

total per ton (of 2000 pounds) on various grades — 

Table XXVIII p. 294 

Train service, cost 65 

supplies and expenses, cost 66 

wages — see Train service. 
Tributary population, estimation of 42 

Valuation, based on capitalization of net earnings 26 

cost of replacing property 23 

par value of stocks and bonds 22 

stock-market quotations 25 

of a railroad's physical property and franchise. . 24 

VALUATION OF RAILWAY PROPERTY.— Chap. IV. 

Velocity, effect on journal and rolling friction 116 

tractive power 130 

head ,...: 124 

(representing the kinetic energy) of trains moving 

at various velocities — Table XX p. 203 

Virtual profile, illustration 125 

Volume of railroad traffic — see Earnings. 

traffic, conditions affecting it. . 46-48 

Wages of engine- and roundhouse-men 62, 77 

Water-supply for locomotives, cost 64 

impurities 79 

methods and cost of pumping 81 

methods for purification 80 

Wear of rails — see Rail wear. 

Weight of cars 91 

Wellington's formulae for train resistance. . 121 

Westinghouse friction draft-gear 98 

Wheel resistance 116 



INDEX. 339 

Wheels, effect of rigidly attaching them to axles 99 

White-oak ties, economics of, compared with other kinds 108 

Wood, use for fuel for locomotives 78 

Wooden tie-plates 110 

Work-cars, cost of repairs and renewals 59 

Yearly wear (in pounds) of outer rails — Sharp curves — Table XVI, p. 159 
of rails on tangents— Table XVII p. 160 



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